NCERT Solutions Class 7 Maths Chapter 1 Large Numbers Around Us

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C L A S S 7 · M AT H S

NCERT Solutions

Chapter 1: Large Numbers
Around Us

NCERT Textbook — Ganita Prakash

BOOK PAGES SECTIONS QUESTIONS MEDIUM

1 – 22 22 83 English

Solutions, notes, sample papers & more at 76 pages

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

CLASS 7 · MATHS · GANITA PRAKASH

NCERT Solutions — Chapter 1: Large Numbers Around
Us
Chapter 1 of Ganita Prakash (Grade 7, Part I) starts with a farmer buying rice seeds and ends with numbers in
the crores. On the way you meet lakhs, crores and arabs, the Indian and American comma systems,
rounding, quick multiplication tricks and a set of calculators called Thoughtful Thousands, Tedious Tens,
Handy Hundreds, Creative Chitti and Systematic Sippy.

TEXTBOOK BOOK PAGES

Ganita Prakash (Class 7) 1 – 22

SECTIONS QUESTIONS

22 83

MEDIUM

English

In-text Questions — Pages 1–2
1.1 A Lakh Varieties!

Q1 Estu wondered, “One lakh! So far I have only tasted 3 varieties. If we tried a new
variety each day, would we even come close to tasting all the varieties in a lifetime
of 100 years?” What do you think? Guess.

No — not even close. One new variety a day for 100 years gives only about 36,500 varieties,
which is roughly a third of a lakh.

Days in 1 year = 365 (ignoring leap years)

Days in 100 years = 365 × 100 = 36,500

Varieties tasted = 36,500 × 1 = 36,500

Still needed = 1,00,000 − 36,500 = 63,500 varieties

Why it happens: A lakh is 1,00,000. A whole 100-year lifetime has only about 36,500
days, so even one variety every single day from birth to death covers barely 36% of a
lakh. That is how big a lakh really is.

Page 1 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Tip: Even with leap days (about 25 extra days per century) the total is only about
36,525 — still nowhere near a lakh.

Q2 But how much is one lakh? Observe the pattern and fill in the boxes given below.

The largest 3-digit number is 999
+1
The smallest 4-digit number is

The largest 4-digit number is
+1
The smallest 5-digit number is

The largest 5-digit number is
+1
The smallest 6-digit number is 1,00,000

1,00,000 is read as “One Lakh”

99,995 99,996 99,998

Page 2 — the chain of statements, and the ten boxes that count on from 99,995.

Each arrow is simply “+ 1”, so every largest number is one step below the next smallest number.

Page 2 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

STATEMENT NUMBER

The largest 3-digit number is 999

The smallest 4-digit number is 1,000

The largest 4-digit number is 9,999

The smallest 5-digit number is 10,000

The largest 5-digit number is 99,999

The smallest 6-digit number is 1,00,000

The chain of ten boxes below it is just counting on by 1:

99,995 → 99,996 → 99,997 → 99,998 → 99,999 → 1,00,000 → 1,00,001 → 1,00,002 →

1,00,003 → 1,00,004

Why it happens: 99,999 is the largest number you can write with 5 digits. Adding 1
makes every 9 roll over to 0 and pushes a fresh 1 into a brand-new place — the lakhs
place. That is exactly how 1,00,000, read as “one lakh”, is born.

Q3 What if a person ate 3 varieties of rice every day? Will they be able to taste all the
lakh varieties in a 100 year lifetime? Find out.

Yes — with 3 varieties a day a person just crosses one lakh.

Days in 100 years = 365 × 100 = 36,500

Varieties in 100 years = 36,500 × 3

= 36,500 × 3 = 1,09,500

1,09,500 > 1,00,000, extra = 9,500 varieties

Why it happens: With 2 varieties a day you get 36,500 × 2 = 73,000, which falls
27,000 short. The jump from 2 to 3 adds another 36,500 and that is what pushes the
total past a lakh.

Page 3 of 76

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Class 7 Maths Chapter 1 Large Numbers Around Us
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co m
m.
Check it yourself: How many varieties a day are needed to reach a lakh in just 50

as e
comday. l
years? Days = 18,250, so you would need 1,00,000 ÷ 18,250 ≈ 5.5, that is at least 6
. a g
em
varieties every
a s
agl

co m
ag
In-text Questions — Page 3
m .
1.1 A Lakh Varieties!
as e
a g l
Choose a number for y. How close to one lakh is the number of days in y years, for
m
Q1

co
m.
the y of your choice?

m as e
ANSWER co
. a g l
e m
g l
Takeasy = 274 — it is the value that lands almost exactly on one lakh.
a
m a s
.co agl
Days in y years = 365 × y

se m
a
365 × 274 = 365 × 200 + 365 × 74

= 73,000 + 27,010 a g l
= 1,00,010 days
co m
m .
1,00,010 − 1,00,000 = only 10 days more than a lakh
m ase
.co a g l
s m other choices:
efew
gl aA
a
Y (YEARS) DAYS = 365 × Y COMPARED WITH 1,00,000
se m
com g l a
m . a
ase
50 18,250 81,750 less

100 36,500agl 63,500 less

200 73,000 27,000 less
co m
m .
as e
com l
274 1,00,010 only 10 more

.300 a g
e m
as
agl
1,09,500 9,500 more

.c
s e m
m a
Why it happens: 1,00,000 ÷ 365 ≈ 273.97. So a little under 274 years contains one

m . co
lakh days. This is exactly Roxie's point on page 4 — “living 1 lakh days would mean
e agl
living for 274 years”.
g l as
a

co m
m .
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.co


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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Figure it Out — Page 3
1.1 A Lakh Varieties!

Q1 According to the 2011 Census, the population of the town of Chintamani was about
75,000. How much less than one lakh is 75,000?

75,000 is 25,000 less than one lakh.

One lakh = 1,00,000

1,00,000 − 75,000

= 25,000

Why it happens: Think in thousands. A lakh is 100 thousands, and 75,000 is 75
thousands. So the gap is 100 − 75 = 25 thousands, that is 25,000. Chintamani in 2011
was three-quarters of a lakh.

Q2 The estimated population of Chintamani in the year 2024 is 1,06,000. How much
more than one lakh is 1,06,000?

1,06,000 is 6,000 more than one lakh.

1,06,000 − 1,00,000

= 6,000

Why it happens: In the Indian system 1,06,000 reads as “one lakh six thousand”. The
comma after the 1 already separates the lakh from the rest, so the part beyond a
lakh is simply 06,000 = 6,000.

Page 5 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q3 By how much did the population of Chintamani increase from 2011 to 2024?

The population went up by 31,000.

Population in 2024 = 1,06,000

Population in 2011 = 75,000

Increase = 1,06,000 − 75,000

= 31,000 people

Why it happens: You can also add the two answers above: 75,000 climbed 25,000 to
reach one lakh, and then a further 6,000 to reach 1,06,000. 25,000 + 6,000 = 31,000
— the same answer, reached without a single borrow.

Did you know? That is an increase of about 41% in 13 years — roughly 2,400 extra
people every year.

In-text Questions — Page 3 (Getting a Feel of Large Numbers)

Page 6 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

1.1 A Lakh Varieties!

Q1 Look at the picture on the right. Somu is 1 metre tall. If each floor is about four
times his height, what is the approximate height of the building?

Hi! I am
Somu.

Page 7 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Page 3 — the building beside the text; Somu waves from a balcony.

The building in the picture has 10 floors, so its height is about 40 metres.

Somu's height = 1 m

Height of one floor = 4 × 1 m = 4 m

Number of floors in the picture = 10

Height of building = 10 × 4 m = 40 m

Why it happens: Somu is standing on the balcony of the topmost floor. Counting the
balconies down the picture gives 10 of them, and each one is a storey four times his
own height. Multiplying 4 m by 10 storeys gives 40 m.

Tip: Remember this 40 m building — the chapter uses it again and again as a
“measuring stick” for the Statue of Unity, the Kunchikal waterfall, Mount Everest and
aeroplanes.

Q2 Which is taller — The Statue of Unity or this building? How much taller? ____________
m.

The Statue of Unity is taller, by 140 m.

Height of Statue of Unity = 180 m

Height of Somu's building = 40 m

Difference = 180 − 40 = 140 m

Why it happens: 180 ÷ 40 = 4.5, so the statue is about four and a half times Somu's
building. The book puts it as “close to 4 times the height of Somu's building”.

Page 8 of 76

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Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

co m
m.
Did you know? The Statue of Unity in Kevadia, Gujarat is the world's tallest statue —

m as e
l
you would have to stack about 4½ ten-storey buildings to match Sardar Patel's head.

m .co a g
l a se
a g
Q3 How much taller is the Kunchikal waterfall than Somu's building? ____________ m.

co m
m . ag
l a se
ag building.
The waterfall is 410 m taller than the

co m
m.
Height of Kunchikal waterfall = 450 m

m as e
.co
Height of Somu's building = 40 m
a g l
a s em = 450 − 40 = 410 m
gl
Difference
a
om a s
. c agl
Why it happens: 450 ÷ 40 = 11.25, so the waterfall is more than eleven times as tall
as the whole building. That is why m
s e a 450 m drop is hard to picture until you compare
it with something you know.gla
a

co m
Did you know? Kunchikal falls, on the Varahi river in Shivamogga district of
m .
m as e
l
Karnataka, is one of India's highest waterfalls.

m .co a g
l a se
ag
Q4 How many floors should Somu's building have to be as high as the waterfall?
se m
____________ .
com g l a
m. a
ase
agl

About 113 floors.

co m
m .
as e
com of one floor = 4 m
Height of waterfall = 450 m
.Height a g l
se m
g l a
a Number of floors = 450 ÷ 4
c
m .
= 112.5
m a s e
e m . co
= 113 floors (you cannot build half a floor, so round up) agl
g l as
a

co m
m .
m ase
.co


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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Why it happens: 112 floors reach only 448 m, which is 2 m short of the waterfall.
One more floor takes the building to 452 m, just past the top of the fall — so 113 is
the smallest whole number of floors that will do.

Try This: The tallest building in India is about 280 m. How many of Somu's floors is
that? 280 ÷ 4 = 70 floors.

In-text Questions — Pages 4–5
Reading and Writing Numbers

Q1 How do you view a lakh — is a lakh big or small?

Both — it depends on what you are counting. A lakh is big for slow things and small for
crowded things.

A LAKH FEELS BIG WHEN… A LAKH FEELS SMALL WHEN…

1 lakh days = 274 years of living 1 lakh people fit in the Ahmedabad cricket stadium

1 lakh people in a line stretch 38 km 80,000–1,20,000 hairs sit on one head

1 lakh varieties of rice is a huge treasure of seeds One female fish can lay nearly a lakh eggs at a time

Why it happens: A number by itself has no size — size comes from comparison. 1
lakh seconds is barely more than a day, but 1 lakh days is nearly three centuries. So
always ask “a lakh of what?” before deciding whether it is big.

Try This: Chintamani's population is about 1 lakh. Could the whole town sit inside
the Ahmedabad stadium? Yes — the stadium seats more than 1 lakh people.

Q2 Write each of the numbers given below in words: (a) 3,00,600 (b) 5,04,085 (c)
27,30,000 (d) 70,53,138

Read the groups from the left: crore, lakh, thousand, then the last three digits.

Page 10 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

NUMBER NUMBER NAME (INDIAN SYSTEM)

(a) 3,00,600 Three lakh six hundred

(b) 5,04,085 Five lakh four thousand eighty five

(c) 27,30,000 Twenty seven lakh thirty thousand

(d) 70,53,138 Seventy lakh fifty three thousand one hundred thirty eight

Why it happens: In 3,00,600 the “00” in the thousands group means no thousands
at all, so that group is simply skipped while reading — you do not say “zero
thousand”. The same happens with the lakh group of 27,30,000, where the last three
digits are 000 and nothing more is read.

Tip: Never insert “and” inside an Indian number name. 5,04,085 is “five lakh four
thousand eighty five”, not “five lakh and four thousand…”.

Q3 Write the corresponding number in the Indian place value system for each of the
following: (a) One lakh twenty three thousand four hundred and fifty six (b) Four
lakh seven thousand seven hundred and four (c) Fifty lakhs five thousand and fifty
(d) Ten lakhs two hundred and thirty five

Write each group in its own place, and fill any missing group with zeroes.

NUMBER NAME NUMBER

(a) One lakh twenty three thousand four hundred and fifty six 1,23,456

(b) Four lakh seven thousand seven hundred and four 4,07,704

(c) Fifty lakhs five thousand and fifty 50,05,050

(d) Ten lakhs two hundred and thirty five 10,00,235

(d) Ten lakhs = 10,00,000
two hundred thirty five = 235

10,00,000 + 235 = 10,00,235

Page 11 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Why it happens: The zeroes are the whole trick. “Ten lakhs two hundred thirty five”
has no thousands, so a 0 must be written in the thousands place — otherwise
10,00,235 would shrink to 10,235.

Check it yourself: Count the digits. Every number between one lakh and ten lakh
has 6 digits; every number between ten lakh and one crore has 7 digits. (c) 50,05,050
has 7 digits — correct for fifty lakh.

Land of Tens — Pages 5–6
1.2 Land of Tens

Q1 The Thoughtful Thousands only has a +1000 button. How many times should it be
pressed to show: (a) Three thousand? 3 times (b) 10,000? (c) Fifty three thousand? (d)
90,000? (e) One Lakh? (f) ______? 153 times (g) How many thousands are required to
make one lakh?

Every press adds 1000, so the number of presses is simply the number divided by 1000.

TARGET WORKING PRESSES

(a) Three thousand 3000 ÷ 1000 3 times

(b) 10,000 10000 ÷ 1000 10 times

(c) Fifty three thousand 53000 ÷ 1000 53 times

(d) 90,000 90000 ÷ 1000 90 times

(e) One lakh 1,00,000 ÷ 1000 100 times

(f) 1,53,000 153 × 1000 153 times

(g) 100 thousands are required to make one lakh.

1 lakh = 1,00,000

1,00,000 ÷ 1,000 = 100

So 100 × 1000 = 1,00,000 ✓

Page 12 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Why it happens: Thoughtful Thousands can only land on multiples of 1000. That is
why every answer above is a whole number — and why this calculator can never
show a number like 3,700 or 97,600.

Q2 The Tedious Tens only has a +10 button. How many times should it be pressed to
show: (a) Five hundred? (b) 780? (c) 1000? (d) 3700? (e) 10,000? (f) One lakh? (g) ______?
435 times

Divide each number by 10.

TARGET WORKING PRESSES

(a) Five hundred 500 ÷ 10 50 times

(b) 780 780 ÷ 10 78 times

(c) 1000 1000 ÷ 10 100 times

(d) 3700 3700 ÷ 10 370 times

(e) 10,000 10000 ÷ 10 1000 times

(f) One lakh 1,00,000 ÷ 10 10,000 times

(g) 4,350 435 × 10 435 times

Why it happens: Dividing by 10 just drops the last zero. That is why the count of
presses looks like the original number with one zero removed — 3700 becomes 370,
and 1,00,000 becomes 10,000.

Tip: Tedious Tens really is tedious — reaching one lakh needs ten thousand presses.
At one press per second that is nearly 3 hours of pressing!

Page 13 of 76

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Class 7 Maths Chapter 1 Large Numbers Around Us
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co m
m.
The Handy Hundreds only has a +100 button. How many times should it be pressed
se
Q3

o m l a
to show: (a) Four hundred? (b) 3,700? (c) 10,000? (d) Fifty three thousand? (e) 90,000?
g are required to
m .c (g) 1,00,000? (h) ______? 582 times (i) How many hundreds
(f) 97,600? a
se ten thousand? (j) How many hundreds are required to make one lakh? (k)
amake
agl Handy Hundreds says, “There are some numbers which Tedious Tens and
Thoughtful Thousands can’t show but I can.” Is this statement true? Think and

co m
. ag
explore.

e m
g l as
a
Divide each number by 100.
m
m .co
e
las
TARGET WORKING PRESSES

co m
m . ag
ase
(a) Four hundred 400 ÷ 100 4 times

agl(b) 3,700 3700 ÷ 100 37 times

m a s
.co agl
(c) 10,000 10000 ÷ 100 100 times

se m 53000 ÷ 100
(d) Fifty three thousand
g l a 530 times

(e) 90,000
a 90000 ÷ 100 900 times

co m
(f) 97,600 97600 ÷ 100
m .
976 times

m l a se 1000 times
.co ag
e(h)m58,200
(g) 1,00,000 100000 ÷ 100

a s
agl 582 × 100 582 times

se m
m lakh. l a
(i) 10,000 ÷ 100 = 100 hundreds make ten thousand.
. coone a g
em
(j) 1,00,000 ÷ 100 = 1000 hundreds make

a s
agl
(k) No, the statement is not true.

Handy Hundreds can show only multiples of 100.
co m
m .
as e
com3,700 = 37 × 100 = 370 × 10
Every multiple of 100 is also a multiple of 10.

.e.g. a g l
se m
g l a
a So Tedious Tens can show every number Handy Hundreds can show.
c
m .
m a s e
e m . co agl
g l as
a

com
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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Why it happens: Handy Hundreds does beat Thoughtful Thousands — 3,700 and
97,600 are impossible for the +1000 button. But it can never beat Tedious Tens,
because 100 is itself ten tens. For the claim to be true, a number would have to be a
multiple of 100 but not a multiple of 10, and no such number exists.

Q4 Creative Chitti is a different kind of calculator. It has the following buttons: +1, +10,
+100, +1000, +10000, +100000 and +1000000. It always has multiple ways of doing
things. To get the number 321, it presses +10 thirty two times and +1 once. Will it
get 321? Alternatively, it can press +100 two times and +10 twelve times and +1
once.

Yes, both ways give exactly 321.

Way 1: (32 × 10) + (1 × 1)

= 320 + 1 = 321 ✓ (33 clicks)

Way 2: (2 × 100) + (12 × 10) + (1 × 1)

= 200 + 120 + 1 = 321 ✓ (15 clicks)

Why it happens: A button press just adds a fixed amount, and addition can be done
in any order. So any combination whose total is 321 works. Chitti is showing that a
number can be broken up in many different ways — 321 = 320 + 1 = 200 + 120 + 1 =
300 + 21 = …

Try This: Find a third way. (3 × 100) + (2 × 10) + (1 × 1) = 321 uses only 6 clicks — the
fewest possible, because 3 + 2 + 1 = 6 is the digit sum.

Page 15 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q5 Two of the many different ways to get 5072 are shown below.

BUTTONS 5072

+10,00,000

+1,00,000

+10,000

+1,000 3

+100 50 20

+10 7

+1 2 72

These two ways can be expressed as: (a) (50 × 100) + (7 × 10) + (2 × 1) = 5072 (b) (3 ×
1000) + (20 × 100) + (72 × 1) = 5072. Find a different way to get 5072 and write an
expression for the same.

Here are three fresh ways, each different from the two given.

Way 1: (5 × 1000) + (7 × 10) + (2 × 1)

= 5000 + 70 + 2 = 5072 (14 clicks)

Way 2: (4 × 1000) + (10 × 100) + (7 × 10) + (2 × 1)

= 4000 + 1000 + 70 + 2 = 5072 (23 clicks)

Way 3: (5 × 1000) + (72 × 1)

= 5000 + 72 = 5072 (77 clicks)

Why it happens: Every way is just a different way of splitting 5072 into pieces worth
1, 10, 100, 1000 … Since 1000 = 10 × 100, you can always trade one press of +1000
for ten presses of +100, or one press of +100 for ten presses of +10. That trade never
changes the total, only the number of clicks.

Page 16 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Tip: Way 1 uses the digits of 5072 itself (5 thousands, 0 hundreds, 7 tens, 2 ones).
That is always the cheapest way — you will prove it on page 7.

Figure it Out — Page 6
1.2 Land of Tens

Q1 For each number given below, write expressions for at least two different ways to
obtain the number through button clicks. Think like Chitti and be creative. (a) 8300
(b) 40629 (c) 56354 (d) 66666 (e) 367813

The first way in each pair uses the digits of the number itself; the second trades one big button
for ten smaller ones.

NUMBER WAY 1 WAY 2

(a) 8300 (8 × 1000) + (3 × 100) (83 × 100)

(b) 40629 (4 × 10000) + (6 × 100) + (2 × 10) + (9 × 1) (40 × 1000) + (62 × 10) + (9 × 1)

(c) 56354 (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1) (56 × 1000) + (35 × 10) + (4 × 1)

(d) 66666 (6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1) (66 × 1000) + (6 × 100) + (66 ×
1)

(e) 367813 (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (36 × 10000) + (78 × 100) + (13
(3 × 1) × 1)

Page 17 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Check (b), Way 2: 40 × 1000 = 40,000

62 × 10 = 620

9×1=9
40,000 + 620 + 9 = 40,629 ✓

Check (e), Way 2: 36 × 10,000 = 3,60,000

78 × 100 = 7,800

13 × 1 = 13

3,60,000 + 7,800 + 13 = 3,67,813 ✓

Why it happens: Because 1000 = 10 × 100 and 100 = 10 × 10, you can always split a
big button into ten of the next smaller one. In (a), one +1000 press was traded for
ten +100 presses: 8 thousands + 3 hundreds became 83 hundreds.

Try This: Write a third way for 8300, such as (5 × 1000) + (33 × 100) = 5000 + 3300 =
8300. How many clicks is that? 5 + 33 = 38.

In-text Questions — Page 7
1.2 Land of Tens

Q1 Creative Chitti has some questions for you — (a) You have to make exactly 30
button presses. What is the largest 3-digit number you can make? What is the
smallest 3-digit number you can make?

Largest = 993. Smallest = 102.

Page 18 of 76

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Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

co m
e m.
Largest: put as many presses as possible on +100.
m l as
.co
(9 × 100) + (8 × 10) + (13 × 1)
m a g
l a se
g
= 900 + 80 + 13 = 993
aPresses = 9 + 8 + 13 = 30 ✓

co m
em . ag
g l
Smallest: put as few presses as possible on +100.
as
(0 × 100) + (8 × 10) + (22 × 1) a

co m
m.
= 0 + 80 + 22 = 102

m as e
.co l
Presses = 0 + 8 + 22 = 30 ✓
a g
se m
g l a
a Why it happens: With 30 presses fixed, moving one press from +1 to +100 adds 99

s
to the number. So to go large you load the +100 button — but you cannot press it 10
m a
.co agl
times (that alone is 1000, a 4-digit number), so 9 is the limit; the remaining 21

a s em
presses must make 93, and 8 tens + 13 ones does it. To go small you avoid +100

agland ones must still reach at least 100, and 8 tens + 22
altogether; 30 presses of tens
ones = 102 is the least such total.

co m
m .
o m l a se
Check it yourself: Could 101 be made? It would need 1 hundred + 0 tens + 1 one (2
.c or 10 tens + 1 one (11 presses) — neither is 30, and
a g no other split of 101
m
aseuses 30 presses. So 102 really is the smallest.
presses)

agl
se m
com g l a
m . a
ase
997 can be made using 25 clicks. Can you make 997 with a different number of

agl
Q2
clicks?

co m
m .
Yes — 997 can be made with many different click counts.
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

25 clicks: (9 × 100) + (9 × 10) + (7 × 1) = 900 + 90 + 7 = 997

Clicks = 9 + 9 + 7 = 25

34 clicks: (9 × 100) + (8 × 10) + (17 × 1) = 900 + 80 + 17 = 997

Clicks = 9 + 8 + 17 = 34

106 clicks: (99 × 10) + (7 × 1) = 990 + 7 = 997

Clicks = 99 + 7 = 106

997 clicks: (997 × 1) = 997

Why it happens: Trading one +100 press for ten +10 presses keeps the total the
same but adds 9 clicks; trading one +10 for ten +1 also adds 9 clicks. So every
possible click count for 997 is 25, 34, 43, 52, … — always 25 plus a multiple of 9. The
smallest is 25 (the digit sum) and the largest is 997.

Page 20 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q3 Systematic Sippy has the buttons +1, +10, +100, +1000, +10000, +100000. It wants to
be used as minimally as possible. How can we get the numbers (a) 5072, (b) 8300
using as few button clicks as possible? Also: the table below shows one way to get
5072 using 23 button clicks.

BUTTONS 5072

+10,00,000

+1,00,000

+10,000

+1,000 5

+100 0

+10 6

+1 12

Is there another way to get 5072 using less than 23 button clicks? Write the
expression for the same.

Yes. 5072 can be made in just 14 clicks, and 8300 in 11 clicks.

(a) 5072 = (5 × 1000) + (0 × 100) + (7 × 10) + (2 × 1)

Clicks = 5 + 0 + 7 + 2 = 14

(b) 8300 = (8 × 1000) + (3 × 100) + (0 × 10) + (0 × 1)

Clicks = 8 + 3 + 0 + 0 = 11

The table's method used (5 × 1000) + (0 × 100) + (6 × 10) + (12 × 1) = 5000 + 60 + 12 = 5072, which
is 5 + 0 + 6 + 12 = 23 clicks. Replacing 6 tens and 12 ones by 7 tens and 2 ones saves 9 clicks.

Why it happens: Every time you use ten small presses where one big press would
do, you waste 9 clicks. The cheapest route is therefore to use each button no more
than 9 times — and that is exactly what the digits of the number tell you to do.

Page 21 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Figure it Out — Page 7
1.2 Land of Tens

MATH TALK

Q1 For the numbers in the previous exercise, find out how to get each number by
making the smallest number of button clicks and write the expression.

Use each digit of the number as the number of presses of its own button.

NUMBER EXPRESSION WITH LEAST CLICKS CLICKS

(a) 8300 (8 × 1000) + (3 × 100) 8 + 3 = 11

(b) 40629 (4 × 10000) + (0 × 1000) + (6 × 100) + (2 × 10) + (9 × 1) 4 + 0 + 6 + 2 + 9 = 21

(c) 56354 (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1) 5 + 6 + 3 + 5 + 4 = 23

(d) 66666 (6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1) 6 × 5 = 30

(e) 367813 (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (3 × 3+6+7+8+1+3=
1) 28

Why it happens: Any press count of 10 or more on a button can be replaced by one
press of the next bigger button plus fewer small ones, saving 9 clicks. Keep doing
this and every button ends up pressed 0 to 9 times — which is precisely the place
value form of the number.

Q2 Do you see any connection between each number and the corresponding smallest
number of button clicks?

Yes — the smallest number of clicks is the sum of the digits of the number.

Page 22 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

NUMBER DIGIT SUM LEAST CLICKS

8300 8 + 3 + 0 + 0 = 11 11

40629 4 + 0 + 6 + 2 + 9 = 21 21

56354 5 + 6 + 3 + 5 + 4 = 23 23

66666 6 + 6 + 6 + 6 + 6 = 30 30

367813 3 + 6 + 7 + 8 + 1 + 3 = 28 28

Why it happens: Each digit says how many of that place value the number contains,
and each of those is exactly one button press. Add up all the digits and you have
counted every press.

Try This: Which 5-digit number needs the most clicks? 99,999 — its digit sum is 45.
Which needs the fewest? 10,000 — just 1 click.

Q3 If you notice, the expressions for the least button clicks also give the Indian place
value notation of the numbers. Think about why this is so.

Because place value notation is itself the “no waste” way of writing a number.

56354 = (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1)
Digits: 5 | 6 | 3 | 5 | 4

Buttons: +10000, +1000, +100, +10, +1

Why it happens: Sippy's buttons are 1, 10, 100, 1000 … — exactly the place values of
our number system. If any button were pressed 10 or more times, ten of those
presses could be swapped for a single press of the next button, cutting 9 clicks. So
the cheapest plan never presses a button more than 9 times, and a count from 0 to 9
for each place value is a digit. That makes the cheapest expression identical to the
expanded form of the number.

Page 23 of 76

as e
Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

co m
m.
Did you know? This is why our system is called a place value system — the position

m as e
l
of a digit tells you which power of ten it is counting.

m .co a g
l a se
a g
In-text Questions — Pages 8–9
com
. ag
1.3 Of Crores and Crores!

se m
l a
Q1 ag button ten times? What number will come up? How
What if we press the +10,00,000
many zeroes will it have? What should we call it?

co m
em.
com — one crore — and it has 7 zeroes. l as

. a g
em
You get 1,00,00,000

a s
agl 10,00,000 × 10

m a s
.co agl
= 1,00,00,000

se m
= 100 lakhs = 1 crore
g l a
1 followed by 7 zeroes a

co m
m .
o m l a se
Why it happens: Multiplying by 10 pushes every digit one place to the left and adds
g that has 7.
.c at the end. Ten lakh already has 6 zeroes, so ten times
a
se m
a zero
a
agl
Tip: Keep a ladder in your head — 1 lakh (5 zeroes) → 10 lakh (6) → 1 crore (7) → 10
se m
crore (8) → 1 arab (9).
com g l a
m . a
ase
agl
How many zeros does a thousand lakh have? _____
m
Q2

. co
em
c o
m g l as
. a
sem
8 zeroes.
a
agl c
m .
m a s e
e m . co agl
g l as
a

com
m .
m ase
.co


a g l Page 24 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

1 thousand lakh = 1,000 × 1,00,000

= 1,000 × 100,000

= 10,00,00,000

= 10 crore

Zeroes: 3 (from 1,000) + 5 (from 1 lakh) = 8

Why it happens: When you multiply two numbers that are each 1 followed by
zeroes, the zeroes simply add up. 103 × 105 = 108.

Q3 How many zeros does a hundred thousand have? ____

5 zeroes.

1 hundred thousand = 100 × 1,000

= 1,00,000

Zeroes: 2 + 3 = 5

And 1,00,000 = 1 lakh

Why it happens: This is the bridge between the two systems. What the American
system calls “one hundred thousand” (written 100,000) the Indian system calls “one
lakh” (written 1,00,000) — same number, different commas and a different name.

Did you know? The word lakh comes from the Sanskrit lakṣha and crore from koṭi.
The Indian system is also used in Nepal, Sri Lanka, Bangladesh, Pakistan, Bhutan,
Maldives, Afghanistan and Myanmar.

Figure it Out — Page 9

Page 25 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

1.3 Of Crores and Crores!

Q1 Read the following numbers in Indian place value notation and write their number
names in both the Indian and American systems: (a) 4050678 (b) 48121620 (c)
20022002 (d) 246813579 (e) 345000543 (f) 1020304050

Place the commas first — 3-2-2-2 from the right for the Indian system, 3-3-3 for the American
system.

NUMBER INDIAN SYSTEM AMERICAN SYSTEM

(a) 4050678 40,50,678 4,050,678
Forty lakh fifty thousand six hundred Four million fifty thousand six hundred seventy
seventy eight eight

(b) 48121620 4,81,21,620 48,121,620
Four crore eighty one lakh twenty one Forty eight million one hundred twenty one
thousand six hundred twenty thousand six hundred twenty

(c) 20022002 2,00,22,002 20,022,002
Two crore twenty two thousand two Twenty million twenty two thousand two

(d) 24,68,13,579 246,813,579
246813579 Twenty four crore sixty eight lakh thirteen Two hundred forty six million eight hundred
thousand five hundred seventy nine thirteen thousand five hundred seventy nine

(e) 34,50,00,543 345,000,543
345000543 Thirty four crore fifty lakh five hundred Three hundred forty five million five hundred
forty three forty three

(f) 1,02,03,04,050 1,020,304,050
1020304050 One arab two crore three lakh four One billion twenty million three hundred four
thousand fifty thousand fifty

Why it happens: The digits never change — only the grouping does. In (c) the Indian
grouping 2,00,22,002 shows “two crore, zero lakh, twenty two thousand, two”, and
the zero lakh group is simply not read aloud.

Tip: A quick check — an Indian-system number with 8 digits is in crores; with 9 digits
it is in ten-crores; with 10 digits it is in arabs.

Page 26 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q2 Write the following numbers in Indian place value notation: (a) One crore one lakh
one thousand ten (b) One billion one million one thousand one (c) Ten crore twenty
lakh thirty thousand forty (d) Nine billion eighty million seven hundred thousand
six hundred

For (b) and (d), first build the number in the American system, then re-comma it the Indian way.

NUMBER NAME INDIAN PLACE VALUE NOTATION

(a) One crore one lakh one thousand ten 1,01,01,010

(b) One billion one million one thousand one 1,00,10,01,001

(c) Ten crore twenty lakh thirty thousand forty 10,20,30,040

(d) Nine billion eighty million seven hundred thousand six hundred 9,08,07,00,600

(b) 1 billion = 1,000,000,000

1 million = 1,000,000

1 thousand = 1,000, and one = 1
Total = 1,001,001,001

Indian commas → 1,00,10,01,001

(d) 9,000,000,000 + 80,000,000 + 700,000 + 600

= 9,080,700,600

Indian commas → 9,08,07,00,600

Why it happens: Both systems write the same digits; only the comma pattern
differs. Write the digits once without any commas, then insert commas from the
right — 3, then 2, 2, 2 for the Indian system.

Page 27 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q3 Compare and write ‘<’, ‘>’ or ‘=’: (a) 30 thousand ____ 3 lakhs (b) 500 lakhs ______ 5
million (c) 800 thousand ____ 8 million (d) 640 crore ______ 60 billion

Bring both sides into plain digits first, then compare.

COMPARISON LEFT IN DIGITS RIGHT IN DIGITS SIGN

(a) 30 thousand ? 3 lakhs 30,000 3,00,000 <

(b) 500 lakhs ? 5 million 5,00,00,000 50,00,000 >

(c) 800 thousand ? 8 million 8,00,000 80,00,000 <

(d) 640 crore ? 60 billion 6,40,00,00,000 60,00,00,00,000 <

(b) 500 lakhs = 500 × 1,00,000 = 5,00,00,000 (5 crore)

5 million = 5 × 10,00,000 = 50,00,000 (50 lakh)

5 crore is ten times 50 lakh, so 500 lakhs > 5 million

(d) 640 crore = 640 × 1,00,00,000 = 6.4 × 109 = 6.4 billion

60 billion = 60 × 109
6.4 billion < 60 billion, so 640 crore < 60 billion

Why it happens: The safest method is to count digits. 6,40,00,00,000 has 10 digits
while 60,00,00,00,000 has 11 — more digits always means a bigger whole number.

Tip: Two conversions worth memorising: 1 million = 10 lakh and 1 billion = 100 crore.

In-text Questions — Page 10

Page 28 of 76

as e
Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

1.4 Exact and Approximate Values
co m
e m.
m l as
.co a g
What do you think of this conversation? Have you read or heard such headlines or
em
Q1

a s
statements? (“1 lakh people visited the book fair.” “If I had not gone, they would

a gl have written 99,999 people visited the book fair last week.”)

. com ag

a s em meant to be exact — it is a rounded figure.
The joke is that the headline number was never

agl
Why it happens: “1 lakh people visited the book fair” means about a lakh — it could

c om
be 97,400 or 1,02,600. One person more or less cannot change a rounded number.
.
The boy is treating an approximate value as if it were an exact count,m
s e which is why

. com sounds funny.
the statement
a gla
a s em
a l
gHeadlines of this kind are everywhere:

s
“Over 50,000 devotees at the temple on Ekadashi.”
m a
“Nearly 1 crore people watched the match.”
m .co agl
l a se
“About 2 lakh vehicles cross the bridge every day.”

a g
Tip: Words like about, nearly, over, around, approximately are the signal that the

co m
.
number has been rounded. When exactness matters — a bank balance, an exam
e m
m as
mark, a train number — those words never appear.

.co a g l
se m
g l a
a
m
Think and share situations where it is appropriate to (a) round up, (b) round down,
se
Q2

com
(c) either rounding up or rounding down is okay and (d) when exact numbers are
g l a
m . a
ase
needed.

ANSWER agl
Round the way that keeps you safe from a shortfall.
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

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m .
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.co


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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

SITUATION EXAMPLE WHY

(a) Round up A school with 732 people orders 750 sweets; Running short is worse than
buying chairs for 118 guests → order 125 having a little extra

(b) Round down A shopkeeper says an item costing ₹470 is A modest claim is safer than an
“around ₹450”; a bag holds 27 kg → “about 25 kg” exaggerated one

(c) Either is Distance from Delhi to Jaipur (268 km) → “about Only a rough idea of size is
fine 270 km”; population of a city needed

(d) Exact Money in a bank account, marks in an exam, Even a difference of 1 changes
numbers votes counted, a phone number, medicine dose the meaning completely

Why it happens: Rounding up is used when a shortage causes trouble (food, chairs,
tickets, cement bags). Rounding down is used when over-promising causes trouble
(a price quote, a time estimate you must beat). And where the number itself is the
answer — money, marks, counts — no rounding is allowed at all.

Try This: Bappi dialled “the rounded off number” for railway enquiry. Why is that a
mistake? Because 139 is an exact helpline number — rounding it to 140 reaches
nobody.

In-text Questions — Page 11 (Nearest Neighbours)
1.4 Exact and Approximate Values

MATH TALK

Q1 Similarly, write the five nearest neighbours for these numbers: (a) 3,87,69,957 (b)
29,05,32,481

Look only at the digits to the right of the place you are rounding to: 5 or more rounds up, less
than 5 rounds down.

Page 30 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

NEAREST… (A) 3,87,69,957 (B) 29,05,32,481

thousand 3,87,70,000 29,05,32,000

ten thousand 3,87,70,000 29,05,30,000

lakh 3,88,00,000 29,05,00,000

ten lakh 3,90,00,000 29,10,00,000

crore 4,00,00,000 29,00,00,000

(a) last 3 digits 957 ≥ 500 → thousand rounds up to 3,87,70,000

last 4 digits 9957 ≥ 5000 → ten thousand also 3,87,70,000

last 5 digits 69,957 ≥ 50,000 → lakh up to 3,88,00,000

last 6 digits 7,69,957 ≥ 5,00,000 → ten lakh up to 3,90,00,000

last 7 digits 87,69,957 ≥ 50,00,000 → crore up to 4,00,00,000

(b) 481 < 500 → down; 2481 < 5000 → down; 32,481 < 50,000 → down;

5,32,481 ≥ 5,00,000 → up; 05,32,481 < 50,00,000 → down

Why it happens: Number (b) is interesting — four of its neighbours round down but
the “nearest ten lakh” rounds up. That is because 5,32,481 is just past half of ten
lakh, while 32,481 is well below half of a lakh. Each place is judged on its own.

Q2 I have a number for which all five nearest neighbours are 5,00,00,000. What could
the number be? How many such numbers are there?

The number must lie between 4,99,99,500 and 5,00,00,499, and there are exactly 1000 such
whole numbers.

Page 31 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Nearest crore = 5,00,00,000 → number lies in 4,50,00,000 to 5,49,99,999

Nearest ten lakh = 5,00,00,000 → 4,95,00,000 to 5,04,99,999

Nearest lakh = 5,00,00,000 → 4,99,50,000 to 5,00,49,999
Nearest ten thousand = 5,00,00,000 → 4,99,95,000 to 5,00,04,999

Nearest thousand = 5,00,00,000 → 4,99,99,500 to 5,00,00,499

Count = 5,00,00,499 − 4,99,99,500 + 1 = 1000 numbers

Why it happens: Each condition is an interval around 5,00,00,000, and the intervals
sit one inside the other — the crore condition is the loosest, the thousand condition
the tightest. So the tightest one, the nearest-thousand band, decides everything,
and every number inside it automatically satisfies the other four.

Check it yourself: Take 5,00,00,300. Nearest thousand = 5,00,00,000 ✓, nearest ten
thousand = 5,00,00,000 ✓, nearest lakh, ten lakh and crore = 5,00,00,000 ✓. All five
agree.

Estimating Sums and Differences — Pages 11–12
1.4 Exact and Approximate Values

Q1 4,63,128 + 4,19,682. Roxie: “The sum is near 8,00,000 and is more than 8,00,000.” Estu:
“The sum is near 9,00,000 and is less than 9,00,000.” (a) Are these estimates correct?
Whose estimate is closer to the sum? (b) Will the sum be greater than 8,50,000 or
less than 8,50,000? Why do you think so? (c) Will the sum be greater than 8,83,128 or
less than 8,83,128? Why do you think so? (d) Exact value of 4,63,128 + 4,19,682 =
___________

(a) Both estimates are correct, but Estu's is closer.

Page 32 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Exact sum = 4,63,128 + 4,19,682 = 8,82,810

Distance from 8,00,000 = 82,810 (Roxie)

Distance from 9,00,000 = 17,190 (Estu)

17,190 < 82,810 → Estu is closer

(b) The sum is greater than 8,50,000.

4,63,128 > 4,50,000 and 4,19,682 > 4,00,000
So the sum > 4,50,000 + 4,00,000 = 8,50,000 ✓

(c) The sum is less than 8,83,128.

8,83,128 = 4,63,128 + 4,20,000

But the second number is 4,19,682, which is 318 less than 4,20,000

So the sum = 8,83,128 − 318 = 8,82,810 < 8,83,128

(d) Exact value = 8,82,810.

Why it happens: You can answer (b) and (c) without adding at all. Replacing each
number by a nearby round number tells you which side of a landmark the sum falls
on — that is the whole point of estimation.

Q2 14,63,128 – 4,90,020. Roxie: “The difference is near 10,00,000 and is less than
10,00,000.” Estu: “The difference is near 9,00,000 and is more than 9,00,000.” (a) Are
these estimates correct? Whose estimate is closer to the difference? (b) Will the
difference be greater than 9,50,000 or less than 9,50,000? Why do you think so? (c)
Will the difference be greater than 9,63,128 or less than 9,63,128? Why do you think
so? (d) Exact value of 14,63,128 – 4,90,020 = __________

(a) Both are correct, but Roxie's estimate is closer.

Page 33 of 76

as e
Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

co m
e m.
Exact difference = 14,63,128 − 4,90,020 = 9,73,108
m l as
.co
Distance from 10,00,000 = 26,892 (Roxie)
m a g
l a se
g
Distance from 9,00,000 = 73,108 (Estu)
a26,892 < 73,108 → Roxie is closer

co m
(b) The difference is greater than 9,50,000.m. ag
l a se
ag
14,63,128 − 5,00,000 = 9,63,128

co m
m.
We are actually subtracting 4,90,020, which is less than 5,00,000

m as e
.co
Subtracting less leaves more, so difference > 9,63,128 > 9,50,000 ✓
a g l
a s em
a g(c)l The difference is greater than 9,63,128.
m a s
9,63,128 = 14,63,128 − 5,00,000
m .co agl
l a se
5,00,000 − 4,90,020 = 9,980
a g
So the difference = 9,63,128 + 9,980 = 9,73,108

co m
m .
m
(d) Exact value = 9,73,108.
as e
.co a g l
s m it happens: In a subtraction, making the number you take away smaller makes
eWhy
gl a
a the answer bigger. Rounding 4,90,020 up to 5,00,000 therefore gives a difference
that is too small — a lower bound you can trust.
se m
com g l a
m . a
e
as9,73,108 + 4,90,020 = 14,63,128 ✓
g l
Check it yourself: Add back:
a

co m
m .
Populations of Cities — Page 13
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

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m .
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.co


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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

1.4 Exact and Approximate Values

Page 35 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q1 Observe the populations of some Indian cities in the table below.

RANK CITY POPULATION (2011) POPULATION (2001)

1 Mumbai 1,24,42,373 1,19,78,450

2 New Delhi 1,10,07,835 98,79,172

3 Bengaluru 84,25,970 43,01,326

4 Hyderabad 68,09,970 36,37,483

5 Ahmedabad 55,70,585 35,20,085

6 Chennai 46,81,087 43,43,645

7 Kolkata 44,86,679 45,72,876

8 Surat 44,67,797 24,33,835

9 Vadodara 35,52,371 16,90,000

10 Pune 31,15,431 25,38,473

11 Jaipur 30,46,163 23,22,575

12 Lucknow 28,15,601 21,85,927

13 Kanpur 27,67,031 25,51,337

14 Nagpur 24,05,665 20,52,066

15 Indore 19,60,631 14,74,968

16 Thane 18,18,872 12,62,551

17 Bhopal 17,98,218 14,37,354

18 Visakhapatnam 17,28,128 13,45,938

19 Pimpri-Chinchwad 17,27,692 10,12,472

20 Patna 16,84,222 13,66,444

From the information given in the table, answer the following questions by
approximation: What is your general observation about this data? Share it with the
class.

Page 36 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Almost every city in the table grew between 2001 and 2011 — several of them enormously —
and only one shrank.

The top two, Mumbai and New Delhi, are the only cities above 1 crore (1,24,42,373 and
1,10,07,835 in 2011).
Bengaluru, Hyderabad, Surat and Vadodara nearly doubled in ten years.
Kolkata is the only city that lost people — it fell from 45,72,876 to 44,86,679, a drop of
about 86,000.
Mumbai grew by only about 4.6 lakh, far less than Bengaluru's 41 lakh, so being the biggest
does not mean growing the fastest.
All 20 cities in the table had more than 16 lakh people in 2011.

Why it happens: Cities with fast-growing industries and IT work (Bengaluru,
Hyderabad, Surat, Pune, Pimpri-Chinchwad) pulled in people from other places,
while already-crowded old cities such as Kolkata and Mumbai grew slowly or not at
all.

Page 37 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q2
RANK CITY POPULATION (2011) POPULATION (2001)

1 Mumbai 1,24,42,373 1,19,78,450

2 New Delhi 1,10,07,835 98,79,172

3 Bengaluru 84,25,970 43,01,326

4 Hyderabad 68,09,970 36,37,483

5 Ahmedabad 55,70,585 35,20,085

6 Chennai 46,81,087 43,43,645

7 Kolkata 44,86,679 45,72,876

8 Surat 44,67,797 24,33,835

9 Vadodara 35,52,371 16,90,000

10 Pune 31,15,431 25,38,473

11 Jaipur 30,46,163 23,22,575

12 Lucknow 28,15,601 21,85,927

13 Kanpur 27,67,031 25,51,337

14 Nagpur 24,05,665 20,52,066

15 Indore 19,60,631 14,74,968

16 Thane 18,18,872 12,62,551

17 Bhopal 17,98,218 14,37,354

18 Visakhapatnam 17,28,128 13,45,938

19 Pimpri-Chinchwad 17,27,692 10,12,472

20 Patna 16,84,222 13,66,444

What is an appropriate title for the above table?

A good title names the what, the where and the when. For example:

“Population of the 20 largest Indian cities, 2001 and 2011”

Page 38 of 76

as e
Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

“Census populations of major Indian cities (2001 vs 2011)”
co m
“Twenty most populous Indian cities and how they grew, 2001–2011”
e m.
m l as
.co a g
a s em
Why it happens: The table has three pieces of information in it — a rank, a city
gl and two population columns dated 2001 and 2011. A title that leaves out the
aname,
years would not tell a reader that the table is about change over time.

com
m . ag
l a se
Q3 agof Pune in 2011? Approximately, by how much has it
How much is the population
increased compared to 2001?

co m
se m.
m l a
o
.c population is 31,15,431, an increase of about 6 lakh overag2001.
se m
Pune's 2011

l a
ag Population in 2011 = 31,15,431

m a s
.co agl
Population in 2001 = 25,38,473

se m
Increase = 31,15,431 − 25,38,473 = 5,76,958
g l a
a
Rounded to the nearest lakh = about 6,00,000 (6 lakh)

co m
m .
o m l a se
Why it happens: Round first and the mental arithmetic is easy: about 31 lakh minus
g it — 5,76,958 rounds to
.c 25 lakh is about 6 lakh. The exact subtraction confirms
a
m
ase6 lakh.
about

agl
se m
com g l a
m . a
ase
Q4 Which city’s population increased the most between 2001 and 2011?

agl

co m
Bengaluru, by 41,24,644 people — more than 41 lakh.
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

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m .
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.co


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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

CITY 2011 2001 INCREASE

Bengaluru 84,25,970 43,01,326 41,24,644

Hyderabad 68,09,970 36,37,483 31,72,487

Ahmedabad 55,70,585 35,20,085 20,50,500

Surat 44,67,797 24,33,835 20,33,962

Vadodara 35,52,371 16,90,000 18,62,371

Mumbai 1,24,42,373 1,19,78,450 4,63,923

Why it happens: Bengaluru added more people in ten years than the entire 2011
population of Pune. Notice that Mumbai, though far larger, added less than 5 lakh —
a big population and a big increase are two different things.

Q5 Are there cities whose population has almost doubled? Which are they?

Yes — Bengaluru, Hyderabad, Surat and Vadodara. Vadodara has more than doubled.

CITY 2001 2011 ROUGHLY HOW MANY TIMES

Vadodara 16,90,000 35,52,371 about 2.1 times

Bengaluru 43,01,326 84,25,970 about 2 times

Hyderabad 36,37,483 68,09,970 about 1.9 times

Surat 24,33,835 44,67,797 about 1.8 times

Pimpri-Chinchwad 10,12,472 17,27,692 about 1.7 times

Why it happens: To check “doubled”, ask whether the 2001 figure doubled is still
smaller than the 2011 figure. For Vadodara, 16,90,000 × 2 = 33,80,000, and 35,52,371
is bigger — so it has more than doubled. For Bengaluru, 43,01,326 × 2 = 86,02,652,
just above 84,25,970 — so it is almost double.

Page 40 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q6 By what number should we multiply Patna’s population to get a number/population
close to that of Mumbai?

By about 7 (more precisely about 7.4).

Patna (2011) = 16,84,222 ≈ 17 lakh

Mumbai (2011) = 1,24,42,373 ≈ 124 lakh

124 ÷ 17 ≈ 7.3

Check: 16,84,222 × 7 = 1,17,89,554 (a bit less than Mumbai)

16,84,222 × 8 = 1,34,73,776 (a bit more than Mumbai)

Why it happens: 7 times Patna falls about 6.5 lakh short and 8 times overshoots by
about 10 lakh, so 7 is the closer whole number. Doing the division exactly gives
1,24,42,373 ÷ 16,84,222 ≈ 7.39.

Tip: For quick comparisons, round both numbers to lakhs first. 124 ÷ 17 is far easier
to judge than 1,24,42,373 ÷ 16,84,222.

In-text Questions — Page 14
1.5 Patterns in Products

MATH TALK

Q1 Using the meaning of multiplication and division, can you explain why multiplying
by 5 is the same as dividing by 2 and multiplying by 10?

Because 5 is half of 10.

Page 41 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

5 = 10 ÷ 2

So n × 5 = n × (10 ÷ 2) = (n ÷ 2) × 10

Roxie's example: 116 × 5

= 116 ÷ 2 × 10

= 58 × 10

= 580

Why it happens: Multiplying by 10 is effortless — just write a zero at the end.
Halving is also easy. So instead of the harder “× 5”, do the two easy steps. The same
idea powers the other shortcuts in this chapter: × 25 = × 100 ÷ 4 (because 25 = 100 ÷
4) and × 125 = × 1000 ÷ 8 (because 125 = 1000 ÷ 8).

Check it yourself: Estu's 824 × 25 = 824 ÷ 4 × 100 = 206 × 100 = 20,600 ✓

Figure it Out — Page 14
1.5 Patterns in Products

Q1 Find quick ways to calculate these products: (a) 2 × 1768 × 50 (b) 72 × 125 [Hint: 125 =
1000 ÷ 8] (c) 125 × 40 × 8 × 25

Regroup the factors so that a 100, 1000 or 10,000 appears.

Page 42 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

(a) 2 × 1768 × 50

= (2 × 50) × 1768

= 100 × 1768

= 1,76,800

(b) 72 × 125

= 72 × (1000 ÷ 8)

= (72 ÷ 8) × 1000

= 9 × 1000

= 9,000

(c) 125 × 40 × 8 × 25
= (125 × 8) × (40 × 25)

= 1000 × 1000

= 10,00,000

Why it happens: Multiplication can be done in any order and in any grouping.
Spotting the pairs that make round numbers — 2 × 50 = 100, 125 × 8 = 1000, 40 × 25
= 1000 — turns a long multiplication into a one-line answer.

Tip: Useful pairs to memorise: 2 × 5, 4 × 25, 8 × 125, 2 × 50, 20 × 5, 40 × 25.

Q2 Calculate these products quickly. (a) 25 × 12 = _____ (b) 25 × 240 = _____ (c) 250 × 120 =
_____ (d) 2500 × 12 = _____ (e) ______ × ______ = 120000000

Replace 25 by 100 ÷ 4, 250 by 1000 ÷ 4 and 2500 by 10,000 ÷ 4.

Page 43 of 76

as e
Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

co m
e m.
(a) 25 × 12 = (100 ÷ 4) × 12 = 100 × 3 = 300
m l as
m .co a g
l a se
g
(b) 25 × 240 = 100 × (240 ÷ 4) = 100 × 60 = 6,000
a

co m
. ag
(c) 250 × 120 = 1000 × (120 ÷ 4) = 1000 × 30 = 30,000
e m
g l as
a
(d) 2500 × 12 = 10,000 × (12 ÷ 4) = 10,000 × 3 = 30,000

co m
em.
as
(e) 12,00,00,000 can be split in many ways. Three easy ones:
m l
.co a g
a s em× 1,00,000 = 12,00,00,000
gl
1200
a 12,000 × 10,000 = 12,00,00,000

m a s
.co agl
1,20,000 × 1,000 = 12,00,00,000

se m
g l a
a
Why it happens: 12,00,00,000 = 12 × 107. Any way of splitting the 12 and the seven
zeroes between two factors will work — the zeroes just move from one factor to the
co m
m .
e
other.
m l as
.co a
m it yourself: (c) and (d) both give 30,000. Makes sense: 250 × 120 and 2500 ×
g
a s eCheck
agl 12 are the same product with a factor of 10 shifted from one number to the other.

se m
com g l a
m . a
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as14–15 (How Long is the Product?)
g
In-text Questions — Pages
a l

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

1.5 Patterns in Products

MATH TALK

Q1 In each of the following boxes, the multiplications produce interesting patterns.
Evaluate them to find the pattern. Extend the multiplications based on the
observed pattern.

11 × 11 = 66 × 61 =
111 × 111 = 666 × 661 =
1111 × 1111 = 6666 × 6661 =

3×5= 101 × 101 =
33 × 35 = 102 × 102 =
333 × 335 = 103 × 103 =

Page 14 — the four boxes of multiplications.

Work each one out and the pattern jumps out.

MULTIPLICATION PRODUCT MULTIPLICATION PRODUCT

11 × 11 121 66 × 61 4,026

111 × 111 12,321 666 × 661 4,40,226

1111 × 1111 12,34,321 6666 × 6661 4,44,02,226

Extend: 11111 × 11111 12,34,54,321 Extend: 66666 × 66661 4,44,40,22,226

3×5 15 101 × 101 10,201

33 × 35 1,155 102 × 102 10,404

333 × 335 1,11,555 103 × 103 10,609

Extend: 3333 × 3335 1,11,15,555 Extend: 104 × 104 10,816

Page 45 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Patterns:

1's: the product counts up and back down — 1, 121, 12321, 1234321, 123454321

6's: 4026 → 440226 → 44402226 — one extra 4, one extra 2 each time
3 & 5: 15 → 1155 → 111555 — as many 1's as 5's

101, 102, 103: 10201, 10404, 10609 — the middle jumps 2, 4, 6 and the end 1, 4, 9 (the

squares)

Why it happens: In the 1's pattern, 1111 × 1111 is really (1000 + 100 + 10 + 1) added
to itself in four shifted rows, so the columns pile up 1, 2, 3, 4, 3, 2, 1 — and since no
column reaches 10, there is no carrying and the counts show up as digits. The
pattern breaks at 1111111111 × 1111111111 because a column would then hold 10.

Check it yourself: 333 × 335 = 333 × 335 = 1,11,555 ✓ — and notice 3333 × 3335 =
1,11,15,555 keeps four 1's and four 5's.

Q2 Observe the number of digits in the two numbers being multiplied and their
product in each case. Is there any connection between the numbers being
multiplied and the number of digits in their product?

Yes. If one number has m digits and the other has n digits, the product has either (m + n − 1) or
(m + n) digits — never anything else.

MULTIPLICATION M+N DIGITS IN PRODUCT

11 × 11 = 121 2+2=4 3=m+n−1

1111 × 1111 = 12,34,321 4+4=8 7=m+n−1

66 × 61 = 4,026 2+2=4 4=m+n

666 × 661 = 4,40,226 3+3=6 6=m+n

3 × 5 = 15 1+1=2 2=m+n

Page 46 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Why it happens: The smallest m-digit number is 10m−1 and the largest is just under
10m. So the product lies between 10m−1 × 10n−1 = 10m+n−2 and 10m × 10n = 10m+n.
That leaves room for exactly two possible digit counts: m + n − 1 or m + n.

Q3 Roxie says that the product of two 2-digit numbers can only be a 3- or a 4-digit
number. Is she correct?

Yes, Roxie is correct.

Smallest 2-digit × smallest 2-digit = 10 × 10 = 100 → 3 digits

Largest 2-digit × largest 2-digit = 99 × 99 = 9,801 → 4 digits

So every such product lies between 100 and 9,801

→ it must have 3 or 4 digits

Why it happens: This matches the rule above with m = n = 2: the product has m + n
− 1 = 3 digits or m + n = 4 digits. Roxie's own argument uses 100 × 100 = 10,000 as a
ceiling, which is a neat trick — since both numbers are below 100, the product must
be below 10,000, i.e. at most 4 digits.

Q4 Should we try all possible multiplications with 2-digit numbers to tell whether
Roxie’s claim is true? Or is there a better way to find out?

There is a far better way — check only the smallest and the largest case. There is no need to
test all 8,100 pairs.

All 2-digit numbers lie between 10 and 99.

So every product lies between 10 × 10 = 100

and 99 × 99 = 9,801.

Both ends have 3 or 4 digits → all products do

Page 47 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Why it happens: Multiplication is “monotonic” — making either factor bigger makes
the product bigger. So squeezing the factors between their smallest and largest
values automatically squeezes the product between the two extreme products.
Checking two cases settles all of them.

Tip: This is a very useful habit in mathematics — instead of testing endless
examples, find the extreme cases and reason about the range in between.

Q5 Can multiplying a 3-digit number with another 3-digit number give a 4-digit
number?

No. The product always has 5 or 6 digits.

Smallest case: 100 × 100 = 10,000 → 5 digits

Largest case: 999 × 999 = 9,98,001 → 6 digits

The smallest possible product, 10,000, is already a 5-digit number.

Why it happens: By the rule, m + n − 1 = 5 and m + n = 6 for two 3-digit numbers. A
4-digit answer would have to be under 10,000, but no pair of 3-digit numbers can
multiply to less than 10,000.

Q6 Can multiplying a 4-digit number with a 2-digit number give a 5-digit number?

Yes.

Smallest case: 1000 × 10 = 10,000 → 5 digits ✓

Largest case: 9999 × 99 = 9,89,901 → 6 digits

Example: 1234 × 12 = 14,808, a 5-digit number

Page 48 of 76

as e
Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

co m
m.
Why it happens: Here m = 4 and n = 2, so the product has m + n − 1 = 5 digits or m +

as e
comnear the small end of their ranges. l
n = 6 digits. Both are possible, and the 5-digit case happens whenever the two
numbers .are a g
a s em
agl

co m
ag
Observe the multiplication statements below. Do you notice any patterns? See if
.
Q7

e m
as
this pattern extends for other numbers as well.

a g l
1-digit × 1-digit = 1-digit or 2-digit

co m
m.
2-digit × 1-digit = 2-digit or 3-digit

m l a sore
.co ag
2-digit × 2-digit = 3-digit 4-digit

a s em3-digit
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× 3-digit = 5-digit or 6-digit
a
5-digit × 5-digit = or

m a s
8-digit ×
em
3-digit .co = or
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12-digit ×
a g13-digit = or

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The blanks follow the same rule: the answer has (m + n − 1) or (m + n) digits.

a s
agl M-DIGIT × N-DIGIT = M+N−1 OR M+N

se m
1-digit × 1-digit
c o m = 1-digit or 2-digit
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2-digit × 1-digit = 2-digit or 3-digit

2-digit ×
a2-digit = 3-digit or 4-digit

coro m
3-digit × 3-digit = 5-digit
m . 6-digit

m as e
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5-digit × 5-digit = 9-digit
a g l or 10-digit

a s em 8-digit
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× 3-digit = 10-digit or 11-digit

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12-digit × 13-digit = 24-digit or 25-digit
s e m
m a
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a

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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Check 5-digit × 5-digit:

10,000 × 10,000 = 10,00,00,000 → 9 digits

99,999 × 99,999 = 9,99,98,00,001 → 10 digits ✓

Why it happens: Notice the odd-looking jump: 2-digit × 2-digit gives 3 or 4 digits,
but 3-digit × 3-digit gives 5 or 6 — never 4. That is because m + n − 1 = 5 for three-
digit numbers, so a 4-digit answer is simply out of reach.

Fascinating Facts about Large Numbers — Pages 16–18
1.5 Patterns in Products

Q1 1250 × 380 = ______________ is the number of kīrtanas composed by Purandaradāsa
according to legends. How many years did he live to compose so many songs? At
what age did he start composing songs? If he composed 4,75,000 songs, how many
songs per year did he have to compose?

The hidden number is 4,75,000.

1250 × 380

= 1250 × 38 × 10

= 47,500 × 10

= 4,75,000

Indian system: four lakh seventy five thousand

American system: four hundred seventy five thousand

How many songs per year? Purandaradāsa is said to have lived about 80 years (1484–1564).

Page 50 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

If he composed for all 80 years:

4,75,000 ÷ 80 = about 5,938 songs a year

= about 16 songs every single day

If he began at about age 30 and composed for 50 years:

4,75,000 ÷ 50 = 9,500 songs a year

= about 26 songs every day

Why it happens: Working out the rate is what shows how astonishing the legend is
— 16 complete songs a day, every day, for eighty years. Most historians therefore
treat 4,75,000 as a traditional figure rather than an exact count; a few hundred of his
kīrtanas survive today.

Did you know? Purandaradāsa, a 15th-century composer and singer, is called the
Pitāmaha (grandfather) of Carnatic music. The graded lessons he designed are still
the first thing a Carnatic student learns.

Q2 2100 × 70,000 = _______________ is the approximate distance in kilometers, between the
Earth and the Sun.

The hidden number is 14,70,00,000 km — about 14 crore 70 lakh kilometres.

2100 × 70,000

= 21 × 7 × 100 × 10,000

= 147 × 10,00,000

= 14,70,00,000

Indian system: fourteen crore seventy lakh

American system: one hundred forty seven million

Page 51 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Why it happens: Strip off the zeroes first — 21 × 7 = 147 — then put back the 2 + 4 =
6 zeroes you removed. This is far quicker than long multiplication.

Did you know? The book adds that the farthest distance is about 152 million km, i.e.
15,20,00,000 km. The Earth's orbit is slightly oval, so the distance changes through
the year.

Q3 6400 × 62,500 = _________________ is the average number of litres of water the Amazon
river discharges into the Atlantic Ocean every second.

The hidden number is 40,00,00,000 litres every second — 40 crore litres.

6400 × 62,500

= 64 × 625 × 100 × 100

= 40,000 × 10,000

= 40,00,00,000

Indian system: forty crore

American system: four hundred million

Why it happens: 64 × 625 is worth spotting: 625 = 10,000 ÷ 16, so 64 × 625 = 64 ÷ 16
× 10,000 = 4 × 10,000 = 40,000. Regrouping again saves all the long multiplication.

Did you know? So much fresh water pours out that drinkable water is found 160 km
out into the open sea. In one second the Amazon delivers enough water to fill about
160 Olympic swimming pools.

Q4 13,95,000 ÷ 150 = _________________ is the distance (in kms) of the longest single-train
journey in the world.

The hidden number is 9,300 km.

Page 52 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

13,95,000 ÷ 150

= 13,95,000 ÷ 15 ÷ 10

= 93,000 ÷ 10

= 9,300

Both systems: nine thousand three hundred

Why it happens: Splitting 150 into 15 × 10 makes the division easy — 1395 ÷ 15 = 93,
so 13,95,000 ÷ 15 = 93,000, and one more division by 10 gives 9,300.

Did you know? That is the Moscow–Vladivostok run on the Trans-Siberian railway,
taking about 7 days. India's longest route, Dibrugarh (Assam) to Kanyakumari (Tamil
Nadu), covers 4,219 km in about 76 hours — a little under half the Russian distance.

Q5 Adult blue whales can weigh more than 10,50,00,000 ÷ 700 = _________________
kilograms.

The hidden number is 1,50,000 kg — one lakh fifty thousand kilograms, or 150 tonnes.

10,50,00,000 ÷ 700

= 10,50,00,000 ÷ 7 ÷ 100

= 1,50,00,000 ÷ 100

= 1,50,000

Indian system: one lakh fifty thousand

American system: one hundred fifty thousand

Why it happens: Cancel the zeroes first. 10,50,00,000 ÷ 100 = 10,50,000, and
10,50,000 ÷ 7 = 1,50,000. Dividing in two easy stages beats one long division.

Page 53 of 76

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Class 7 Maths Chapter 1 Large Numbers Around Us
a g l AglaSem · NCERT Solutions

co m
m.
Did you know? A newborn blue whale already weighs about 2,700 kg — as much as

m l a se
an adult hippopotamus. Its heart alone is about 700 kg, and it eats up to 3,500 kg of
o
krill a day..cEven Argentinosaurus, the largest known land animal,
a gis estimated at only
m
se kg.
l a
ag
90,000

o m
e
. c
m was the weight, in tonnes, of global plastic ag
s
52,00,00,00,000 ÷ 130 = _________________
a
Q6

agl
waste generated in the year 2021.

co m
em.
as
The hidden number is 40,00,00,000 tonnes — 40 crore tonnes.
m l
.co a g
a s em
l
52,00,00,00,000 ÷ 130
a g = 52,00,00,00,000 ÷ 13 ÷ 10

m a s
.co agl
= 4,00,00,00,000 ÷ 10

se m
= 40,00,00,000
g l a
a
Indian system: forty crore
co m
m .
m as e
l
American system: four hundred million
.co a g
a s em
agl Why it happens: 52 ÷ 13 = 4 exactly, so the whole division collapses to moving the
decimal — no long division needed at all.
se m
com g l a
m . a
ase
agl
Large number fact: A single gram of healthy soil can hold 10 crore to 1 arab (100
million to 1 billion) bacteria and 1 lakh to 10 lakh fungi. Share such large-number
facts with your class.
co m
m .
m as e
.co a g l
se m Questions — Pages 18–19
a
In-text
ag l
.c
s e m
m a
e m . co agl
g l as
a

co m
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.co


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Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

1.6 Did You Ever Wonder…?

Q1 “Could the entire population of Mumbai fit into 1 lakh buses?” What do you think?
How can we find out?

No, it could not. One lakh buses hold about 50 lakh people, but Mumbai has more than 1 crore
24 lakh.

Assume 1 bus holds 50 people.
1 lakh buses hold = 1,00,000 × 50

= 50,00,000 = 50 lakh people

Population of Mumbai (2011) = 1,24,42,373

1,24,42,373 > 50,00,000

Left standing = 1,24,42,373 − 50,00,000 = 74,42,373 people

Why it happens: The method is what matters — make a sensible assumption (50
seats per bus), multiply, then compare with the real figure. To fit all of Mumbai you
would need 1,24,42,373 ÷ 50 ≈ 2,48,848 buses, nearly 2½ lakh.

Q2 The RMS Titanic ship carried about 2500 passengers. Can the population of Mumbai
fit into 5000 such ships?

Yes — just barely.

Page 55 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Capacity = 5000 × 2500

= 5 × 25 × 1000 × 100

= 125 × 1,00,000
= 1,25,00,000 people (1 crore 25 lakh)

Population of Mumbai = 1,24,42,373

1,24,42,373 < 1,25,00,000 ✓

Space to spare = 57,627 places

Why it happens: It is a very close call — the ships hold only about 58,000 more than
Mumbai's population, less than half a percent extra. Had we used Mumbai's present-
day population instead of the 2011 census figure, the answer might well flip to “no”.

Q3 Roxie wondered, “If I could travel 100 kilometers every day, could I reach the Moon
in 10 years?” (The distance between the Earth and the Moon is 3,84,400 km.) How far
would she have travelled in a year? How far would she have travelled in 10 years?

No — after 10 years she would still be about 19,400 km short.

Distance in 1 year = 100 × 365

= 36,500 km

Distance in 10 years = 36,500 × 10

= 3,65,000 km

Distance to the Moon = 3,84,400 km

Short by = 3,84,400 − 3,65,000 = 19,400 km

Page 56 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Why it happens: Doing it in stages — first per year, then per 10 years — keeps the
numbers small and manageable. You can use this staged method for any large
calculation.

Check it yourself: How long would the whole trip take? 3,84,400 ÷ 36,500 ≈ 10.5
years — so a little over ten and a half years.

Q4 Find out if you can reach the Sun in a lifetime, if you travel 1000 kilometers every
day. (You had written down the distance between the Earth and the Sun in a
previous exercise.)

No. The journey would take about 403 years — far more than a lifetime.

Distance to the Sun = 14,70,00,000 km (from page 16)

Distance in 1 year = 1000 × 365 = 3,65,000 km

Years needed = 14,70,00,000 ÷ 3,65,000

= 1,47,000 ÷ 365

≈ 402.7 years

Why it happens: A human lifetime is at most about 100 years, so you would cover
only 100 × 3,65,000 = 3,65,00,000 km — roughly a quarter of the way. You would
need four full lifetimes travelling 1000 km every single day.

Tip: Cancel the common zeroes before dividing: 14,70,00,000 ÷ 3,65,000 becomes
1,47,000 ÷ 365, which is much friendlier.

Page 57 of 76

Class 7 Maths Chapter 1 Large Numbers Around Us AglaSem · NCERT Solutions

Q5 Make necessary reasonable assumptions and answer the questions below: (a) If a
single sheet of paper weighs 5 grams, could you lift one lakh sheets of paper
together at the same time? (b) If 250 babies are born every minute across the world,
will a million babies be born in a day? (c) Can you count 1 million coins in a day?
Assume you can count 1 coin every second.

All three answers are no.

(a) Weight = 1,00,000 × 5 g

= 5,00,000 g = 500 kg

A person can lift perhaps 40–50 kg, so no — 500 kg is about the weight of 8 adults.

(b) Minutes in a day = 60 × 24 = 1,440
Babies in a day = 250 × 1,440 = 3,60,000

1 million = 10,00,000

3,60,000 < 10,00,000 → no, only about a third of a million.

(c) Seconds in a day = 60 × 60 × 24 = 86,400

So at most 86,400 coins a day.

86,400 < 10,00,000 → no, not even a tenth of a million.

Why it happens: Part (c) hides a very useful fact — a day is only 86,400 seconds.
Counting a million things at one per second would take 10,00,000 ÷ 86,400 ≈ 11.6
days without a single break for sleep.

Try This: Make up your own questions in the same style. “Could all the students in
your school stand shoulder to shoulder across a 1 km road?” “Would a lakh one-
rupee coins fill your school bag?”

Figure it Out — Pages 19–21

Page 58 of 76

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Class 7 Maths Chapter 1 Large Numbers Around Us
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1.6 Did You Ever Wonder…?
co m
e m.
m as
TRY THIS

.co a g l
a s em all digits from 0 – 9 exactly once (the first digit cannot be 0) to create a 10-
gl
Using
a
Q1
digit number, write the — (a) Largest multiple of 5 (b) Smallest even number

co m
e m . ag
(a) 98,76,54,32,10 (b) 1,02,34,56,798
g l as
a
(a) A multiple of 5 must end in 0 or 5.
co m
em.
omin decreasing order: 9,8,7,6,5,4,3,2,1 as
Ending in 0 is better — it frees the 5 for a higher place.

Put the.crest a g l
a s em
a gl Largest = 9876543210
m a s
em
(b) An even number must end in 0, 2, 4, 6 or 8. .co agl
a s
agl
To be small, the front should read 1,0,2,3,4,…

Ending in 8 keeps the front smallest: 102345679 | 8

co m
Smallest = 1023456798
m .
m as e
.co a g l
s m it happens: In (b), why not end in 0? Because 0 is the most valuable digit for
eWhy
gl a
a making the front small — it belongs right after the leading 1. Ending in 2, 4 or 6
would force a bigger digit into an earlier place. Ending in 8 leaves 0,1,2,3,4,5,6,7,9 to
se m
com possible front. g l a
.
be arranged as 102345679, the smallest
a
a s em
agl ÷ 2 = 511728399, so it is even ✓, and it uses each of
Check it yourself: 1023456798
0–9 exactly once ✓.
co m
m .
m as e
.co a g l
a s emQ2
gl
The number 10,30,285 in words is Ten lakhs thirty thousand two hundred eighty
a five, which has 42 letters. Give a 7-digit number name which has the maximum
c
m .
e
number of letters.
m a s
m . co agl
l a se
ag lakh seventy seven thousand seven hundred seventy seven” — with
77,77,777 — “seventy seven
60 letters.

co m
m .
m ase
.co


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