NCERT Solutions for Class 6 Maths Chapter 8 Decimals

NCERT
SOLUTIONS
CLASS - 6TH

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Class : 6th
Subject : Maths
Chapter : 8
Chapter Name : DECIMALS

Exercise 8.1

Q1 Write the following as numbers in the given table.

Answer. It may be observed that

Page : 167 , Block Name : Exercise 8.1

Q2 Write the following decimals in the place value table.

(a) 19.4
(b) 0.3
(c) 10.6
(d) 205.9

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Answer.

Page : 168 , Block Name : Exercise 8.1

Q3 Write each of the following as decimals :
(a) Seven-tenths
(b) Two tens and nine-tenths
(c) Fourteen point six
(d) One hundred and two ones
(e) Six hundred point eight

7
Answer. (a) Seven-tenths = 10 = 0.7

9
(b) Two tens and mne-tenths = = 20 + 10 = 20.9

(c) Fourteen point six = 14.6

(d) One hundred and two ones = 100 + 2 = 102.0

(e) Six hundred point eight = 600.8

Page : 168 , Block Name : Exercise 8.1

Q4 Write each of the following as decimals:

5
(a) 10

7
(b) 3 + 10

1
(c) 200 + 60 + 5 + 10

8
(d) 70 + 10

88
(e) 10

2
(f) 4 10

(g) 32

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

(h) 25

(i) 12
5

3
(j) 3 5

(k) 4 12

5
Answer. (a) 10 = 0.5

7
(b) 3 + 10 = 3 + 0.7 = 3.7

1
(c) 200 + 60 + 5 + 10 = 265 + 0.1 = 265.1

8
(d) 70 + 10 = 70 + 0.8 = 70.8

88 80 8
(e) 10 = 10 + 10 = 8 + 0.8 = 8.8

2 2
(f) 4 10 = 4 + 10 = 4 + 0.2 = 4.2

3 2+1
(g) 2 = 2
= 22 + 12 = 1 + 0.5 = 1.5

(h) 25 = 0.4

10+2
(i) 12
5
= 5
= 10
5
+ 25 = 2 + 0.4 = 2.4

3 3
(j) 3 5 = 3 + 5 = 3 + 0.6 = 3.6

(k) 4 12 = 4 + 12 = 4 + 0.5 = 4.5

Page : 168 , Block Name : Exercise 8.1

Q5 Write the following decimals as fractions. Reduce the fractions to lowest form.

(a) 0.6

(b) 2.5

(c) 1.0

(d) 3.8

(e) 13.7

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

(f) 21.2

(g) 6.4

6
Answer. (a) 0.6 = 10 = 35

25 5
(b) 2.5 = 10 = 2

(c) 1.0 = 1

38 19
(d) 3.8 = 10 = 5

137
(e) 13.7 = 10

106
(f) 21.2 = 212
10
= 5

64 32
(g) 6.4 = 10 = 5

Page : 168 , Block Name : Exercise 8.1

Q6 Express the following as cm using decimals.

(a) 2 mm
(b) 30 mm
(c) 116 mm
(d) 4 cm 2 mm
(e) 162 mm
(f) 83 mm

Answer. It is known that 1cm = 10 mm

2
(a) 2mm = 10 cm = 0.2cm

30
(b) 30mm = 10 cm = 3.0cm

116
(c) 116mm = 10
cm = 11.6cm

(d) 4cm2mm = (4 + 10
2
) cm = 4.2cm

162
(e) 162mm = 10
cm = 16.2cm

83
(f) 83mm = 10 cm = 8.3cm

Page : 168 , Block Name : Exercise 8.1

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Q7 Between which two whole numbers on the number line are the given numbers lie? Which of these
whole numbers is nearer the number?

(a) 0.8
(b) 5.1
(c) 2.6
(d) 6.4
(e) 9.1
(f) 4.9

Answer. (a) 0.8 lies between 0 and 1, and is nearer to 1

(b) 5.1 lies between 5 and 6, and is nearer to 5

(c) 2.6 lies between 2 and 3, and is nearer to 3

(d) 6.4 lies between 0 and 7, and is nearer to 6

(e) 9.1 lies between 0 and 10, and is nearer to 9

(f) 4.9 lies between 0 and 5, and is nearer to 5

Page : 168 , Block Name : Exercise 8.1

Q8 Show the following numbers on the number line.

(a) 0.2
(b) 1.9
(c) 1.1
(d) 2.5

Answer. (a) 0.2 represents a point between O and 1 on number line, such that the
space between O and 1 is divided into 10 equal parts. Hence, each equal part will be
equal to one-tenth. Now, 0.2 is the second point between o and 1.

(b) 1.9 represents a point between 1 and 2 on number line, such that the
space between 1 and 2 is divided into 10 equal parts. Hence, each equal pan will be
equal to one-tenth. Now, 1.9 is the ninth point between 1 and 2.

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

(c) 1.1 represents a point between 1 and 2 on number line, such that the
space between 1 and 2 is divided into 10 equal parts. Hence, each equal part will be
equal to one-tenth. Now, 1.1 is the �rst point between 1 and 2.

(d) 2.5 represents a point between 2 and 3 on number line, such that the
space between 2 and 3 is divided into 10 equal parts. Hence, each equal part will be
equal to one-tenth. Now, 2.5 is the �fth point between 2 and 3.

Page : 168 , Block Name : Exercise 8.1

Q9 Write the decimal number represented by the points A, B, C, D on the given number line.

Answer. point A represents 0.8.

Point 3 represents 1.3.

Point C represents 2.2.

Point O represents 2.9.

Page : 168 , Block Name : Exercise 8.1

Q10 (a) The length of Ramesh’s notebook is 9 cm 5 mm. What will be its length in cm?

(b) The length of a young gram plant is 65 mm. Express its length in cm.

Answer. (a) The length of Ramesh's notebook is 9 cm 5 mm.

Therefore, the length in cm is (9 + 10 ) cm = 9.5cm
5

(b) The length of a gram plant is 65 mm.

65
Therefore, the length in cm is 10 = 6.5cm

Page 6 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Page : 168 , Block Name : Exercise 8.1

Exercise 8.2

Q1 Complete the table with the help of these boxes and use decimals to write the number.

Answer.

Page : 173 , Block Name : Exercise 8.2

Q2 Write the numbers given in the following place value table in decimal form

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

2 5
Answer. (a) 3 + 10 + 100 = 3 + 0.2 + 0.05 = 3.25

6 3
(b) 100 + 2 + 10 + 100 = 102 + 0.6 + 0.03 = 102.63

2 5
(c) 30 + 100 + 1000 = 30 + 0.02 + 0.005 = 30.025

9 2
(d) 200 + 10 + 1 + 10 + 1000 = 211 + 0.9 + 0.002 = 211.902

2 4 1
(e) 10 + 2 + 10 + 100 + 1000 = 12 + 0.2 + 0.04 + 0.001 = 12.241

Page : 173 , Block Name : Exercise 8.2

Q3 Write the following decimals in the place value table.
(a) 0.29
(b) 2.08
(c) 19.60
(d) 148.32
(e) 200.812

2 9
Answer. (a) 0.29 = 0.2 + 0.09 = 10 + 100

8
(b) 2.08 = 2 + 0.08 = 2 + 100

6
(c) 19.60 = 19 + 0.60 = 10 + 9 + 10

3 2
(d) 148.32 = 148 + 0.3 + 0.02 = 100 + 40 + 8 + 10 + 100

8
1 2
(e) 200.812 = 200 + 0.8 + 0.01 + 0.002 = 200 + 10 + 100 + 1000

Page 8 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Page : 174 , Block Name : Exercise 8.2

Q4 Write each of the following as decimals.

4 1
(a) 20 + 9 + 10 + 100

5
(b) 137 + 100

7 6 4
(c) 10 + 100 + 1000

2 6
(d) 23 + 10 + 1000

9
(e) 700 + 20 + 5 + 100

4 1
Answer. (a) 20 + 9 + 10 + 100 = 29 + 0.4 + 0.01 = 29.41

5
(b) 137 + 100 = 137 + 0.05 = 137.05

7 6 4
(c) 10 + 100 + 1000 = 0.7 + 0.06 + 0.004 = 0.764

2 6
(d) 23 + 10 + 1000 = 23 + 0.2 + 0.006 = 23.206

9
(e) 700 + 20 + 5 + 100 = 725 + 0.09 = 725.09

Page : 174 , Block Name : Exercise 8.2

Q5 Write each of the following decimals in words.
(a) 0.03
(b) 1.20
(c) 108.56
(d) 10.07
(e) 0.032
(f) 5.008

Answer. (a) 0.03 = zero point zero three

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

(b) 1.20 = one point two zero

(c) 108.56 = one hundred eight point �ve six

(d) 10.07 = ten point zero seven

(e) 0.032 = zero point zero three two

(f) 5.008 = �ve point zero zero eight

Page : 174 , Block Name : Exercise 8.2

Q6 Between which two numbers in tenths place on the number line does each of the given number
lie?

(a) 0.06
(b) 0.45
(c) 0.19
(d) 0.66
(e) 0.92
(f) 0.57

Answer. (a) 0.06 → 0 and 0.1

(b) 0.45 → 0.4 and 0.5

(c) 0.19 → 0.1 and 0.2

(d) 0.66 → 0.6 and 0.7

(e) 0.92 → 0.9 and 1.0

(f) 0.57 → 0.5 and 0.6

Page : 174 , Block Name : Exercise 8.2

Q7 Write as fractions in lowest terms.

(a) 0.60
(b) 0.05
(c) 0.75
(d) 0.18
(e) 0.25
(f) 0.125
(g) 0.066

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

60 6
Answer. (a) 0.60 = 100 = 10 = 35

5 1
(b) 0.05 = 100 = 20

75 3
(c) 0.75 = 100 = 4

18 9
(d) 0.18 = 100 = 50

25
(e) 0.25 = 100 = 14

66 33
(f) 0.066 = 1000 = 500

Page : 174 , Block Name : Exercise 8.2

Exercise 8.3

Q1 Which is greater?
(a) 0.3 or 0.4
(b) 0.07 or 0.02
(c) 3 or 0.8
(d) 0.5 or 0.05
(e) 1.23 or 1.2
(f) 0.099 or 0.19
(g) 1.5 or 1.50
(h) 1.431 or 1.490
(i) 3.3 or 3.300
(j) 5.64 or 5.603

Answer. (a) 0.3 or 0.4

The whole parts of these numbers are same. It can be seen that the tenth part of 0.4 Is
greater than that of 0.3.

Hence, 0.4 > 0.3

(b) 0.07 and 0.02

Here, both numbers have same parts up to the tenth place. However, the hundredth pan
of 0.07 is greater than that of 0.02.

Hence, 0.07 > 0.02

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

(c) 3 or 0.8

It can be seen that the whole part of 3 is greater than that of 0.8.

Hence, 3 0.8

(d) 0.5 or 0.05

The whole parts of these numbers are same. It can be seen that the tenth part of 0.5 is
greater than that of 0.05.

Hence, 0.5 > O.O5

(e) 1.23 or 1.20

Here, both numbers have same parts up to the tenth place. However, the hundredth part
of 1.23 is greater than that of 1.20.

Hence, 1.23 > 1.20

(f) 0.099 or 0.19

The whole parts of these numbers are same. It can be seen that the tenth part of 0.19 is
greater than that of 0.099.

Hence, 0.099 < 0.19

(g) 1.5 or 1.50

Here, both numbers have the same pmts up to the tenth place. Also, there is no digit at
hundredth place of 1.5. This implies that this digit Will be 0, which is same as the digit at
the hundredth place of 1.50. Therefore, both these numbers are equal.

(h) 1.431 or 1.490

Here, both numbers have the same pans up to the tenth place. However, the hundredth
part of 1.490 is greater than that of 1.431.

Hence, 1.431 < 1.490

(i) 3.3 or 3.300

Page 12 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Here, both numbers have the same pans up to the tenth place. Also, there is no digit at
hundredth and thousandth place of 3.3. This implies that these digits are 0, which are
the same as the digits at the hundredth and thousandth place of 3.300. Therefore, both
these numbers are equal.

(j) 5.64 or 5.603

Here, both numbers have the same parts up to the tenth place. However, the hundredth
part of 5.64 is greater than that of 5.603.

Hence, 5.640 > 5.603

Page : 175 , Block Name : Exercise 8.3

Q2 Make �ve more examples and �nd the greater number from them.

Anwer. DIY

Page : 175 , Block Name : Exercise 8.3

Exercise 8.4

Q1 Express as rupees using decimals.
(a) 5 paise
(b) 75 paise
(c) 20 paise
(d) 50 rupees 90 paise
(e) 725 paise

Answer. It is known that there are 100 paise in 1 rupee.

5
(a) 5 paise = 100 rupees = Re 0.05

75
(b) 75 paise = 100 rupees = Re 0.75

20
(c) 20 paise = 100 rupees = Re 0.20

(d) 50 rupees 90 paise = (50 + 100 ) rupees = Rs 50.90
90

725
(e) 725 paise = 100 rupees = Rs 7.25

Page : 177 , Block Name : Exercise 8.4

Page 13 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Q2 Express as metres using decimals.
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9 m 7 cm
(e) 419 cm

Answer. It is known that there are 100 cm in 1 metre.

15
(a) 15cm = 100 m = 0.15m

6
(b) 6cm = 100 m = 0.06m

(c) 2m45cm = (2 + 100 ) m = 2.45m
45

(d) 9m7cm = (9 + 100 ) m = 9.07m
7

419
(e) 419cm = 100 m = 4.19m

Page : 177 , Block Name : Exercise 8.4

Q3 Express as cm using decimals.
(a) 5 mm
(b) 60 mm
(c) 164 mm
(d) 9 cm 8 mm
(e) 93 mm

Answer. It is known that there are 10 mm in 1 cm

5
(a) 5mm = 10 cm = 0.5cm

60
(b) 60mm = 10 cm = 6.0cm

164
(c) 164mm = 10
cm = 16.4cm

(d) 9cm8mm = (9 + 10 ) cm = 9.8cm
8

93
(e) 93mm = 10 cm = 9.3cm

Page : 177 , Block Name : Exercise 8.4

Q4 Express as km using decimals.
(a) 8 m

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

(b) 88 m
(c) 8888 m
(d) 70 km 5 m

Answer. It is known that there are 1000 metres in 1 km.

8
(a) 8m = 1000 km = 0.008km

88
(b) 88m = 1000 km = 0.088km

8888
(c) 8888m = 1000 km = 8.888km

(d) 70km5m = (70 + 1000 ) km = 70.005km
5

Page : 177 , Block Name : Exercise 8.4

Q5 Express as kg using decimals.
(a) 2 g
(b) 100 g
(c) 3750 g
(d) 5 kg 8 g
(e) 26 kg 50 g

Answer. It is known that there are 1000 grams in 1 kg.

2
(a) 2g = 1000 kg = 0.002kg

100
(b) 100g = 1000 kg = 0.1kg

3750
(c) 3750g = 1000 kg = 3.750kg

(d) 5 kg 8g = (5 + 1000 ) kg = 5.008kg
8

(e) 26kg50g = (26 + 1000 ) kg = 26.050kg
50

Page : 177 , Block Name : Exercise 8.4

Exercise 8.5

Q1 Find the sum in each of the following :
(a) 0.007 + 8.5 + 30.08
(b) 15 + 0.632 + 13.8

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

(c) 27.076 + 0.55 + 0.004
(d) 25.65 + 9.005 + 3.7
(e) 0.75 + 10.425 + 2
(f) 280.69 + 25.2 + 38

Answer. (a) 0.007 + 8.5 + 30.08
0.007
8.500
+ 30.080
38.587

(b) 15 + 0.632 + 13.8
15.000
0.632
+ 13.800
29.432

(c) 27.076 + 0.55 + 0.004
27.076
0.550
+ 0.004
27.630

(d) 25.65 + 9.005 + 3.7
25.650
9.005
3.700
+ 38.355

(e) 0.75 + 10.425 + 2
0.750
10.425
2.000
+ 13.175

(f) 280.69 + 25.2 + 38
280.69
25.20
38.00
+ 343.89

Page 16 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Page : 179 , Block Name : Exercise 8.5

Q2 Rashid spent Rs. 35.75 for Maths book and Rs. 32.60 for Science book. Find the total amount spent
by Rashid.

Answer. pnce of Maths book = RS. 35.75

Price of Science book = Rs. 32.60

Total amount spent by Rashid is
35.75
+32.60
68.35

Therefore, the amount spent by Rashid is Rs. 68.35

Page : 179 , Block Name : Exercise 8.5

Q3 Radhika’s mother gave her Rs. 10.50 and her father gave her Rs. 15.80, �nd the total amount given
to Radhika by the parents.

Answer. Amount given by mother = Rs. 10.50

Amount given by mother = Rs. 15.80

Total amount given by parents is
10.05
+15.80
26.30

Therefore, the amount given by her parents is Rs. 26.30.

Page : 179 , Block Name : Exercise 8.5

Q4 Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find the total
length of cloth bought by her.

Answer. Cloth for shirt = 3 m 20 cm

Cloth for trouser = 2 m 5 cm

Total length of cloth is
3.20
+2.05
5.25

Page 17 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Hence, the total length of cloth bought by her is 5.25 m.

Page : 179 , Block Name : Exercise 8.5

Q5 Naresh walked 2 km 35 m in the morning and 1 km 7 m in the evening. How much distance did he
walk in all?

Answer. Distance walked in the morning = 2 km 35 m
= (2 + 1000
35
) km
= 2.035km

Distance walked in the evening = 1 km 7 m
= (1 + 1000
7
) km
= 1.007km

Total distance walked by him is
2.035
+1.007
3.042km

Page : 179 , Block Name : Exercise 8.5

Q6 Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot in order to reach her
school. How far is her school from her residence?

Answer. Distance travelled by bus = 15 km 268 m
= (15 + 1000
268
) km
= 15.268km

Distance travelled by car = 7 km 7 m
= (7 + 1000
7
) km
= 7.007km

Distance travelled on foot = 500 m
500
= km
1000
= 0.500km

Total distance of school from her residence is
15.268
7.007
+0.500
22.775km

Page 18 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Page : 180 , Block Name : Exercise 8.5

Q7 Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850g �our. Find the total weight of his
purchases.

Answer. Weight of rice = 5 kg 400 g = (5 + 1000 ) kg = 5.400kg
400

Weight of sugar = 2kg 20 g = (2 + 1000 ) kg = 2.020kg
20

Weight of �our = 10 kg 850 g = (10 + 1000 ) kg = 10.850kg
850

Total weight of his purchases is
5.400
2.020
10.850
+ 18.270km

Page : 180 , Block Name : Exercise 8.5

Exercise 8.6

Q1 Subtract :
(a) Rs. 18.25 from Rs. 20.75
(b) 202.54 m from 250 m
(c) Rs. 5.36 from Rs. 8.40
(d) 2.051 km from 5.206 km
(e) 0.314 kg from 2.107 kg

Answer. (a) Rs. 20.75 - Rs. 18.25
20.75
− 18.25
2.50

(b) 250 m - 202.54 m
250.00
− 202.54
47.46

(c) Rs. 8.40 - Rs. 5.36
8.40
− 5.36
3.04

Page 19 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

(d) 5. 206 km - 2.051 km
5.206
− 2.051
3.155

(e) 2.107 kg - 0.314 kg
2.107
− 0.314
1.793

Page : 181 , Block Name : Exercise 8.6

Q2 Find the value of :
(a) 9.756 – 6.28
(b) 21.05 – 15.27
(c) 18.5 – 6.79
(d) 11.6 – 9.847

9.756
Answer. (a) −6.280
3.476

21.05
(b) −15.27
5.78

18.50
(c) −6.79
11.71

11.600
(d) −9.847
1.753

Page : 181 , Block Name : Exercise 8.6

Q3 Raju bought a book for Rs. 35.65. He gave Rs. 50 to the shopkeeper. How much money did he get
back from the shopkeeper?

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Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Answer. Money given to shopkeeper = Rs. 50.00

Cost of book = Rs. 35.65

Money that raju will get back will be the difference of these two.

Hence, money that rju will get back is
50.00
−35.65
14.35

Therefore, he will get back Rs. 14.35

Page : 182 , Block Name : Exercise 8.6

Q4 Rani had Rs. 18.50. She bought one ice-cream for Rs. 11.75. How much money does she have now?

Answer. Money with rani = Rs. 18.50

The money left with rani will be the difference of these two.

Hence, the money left is
18.50
−11.75
6.75

Page : 182 , Block Name : Exercise 8.6

Q5 Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth from this for making a curtain.
How much cloth is left with her?

Answer. Length of cloth = 20 m 5 cm = 20.05 m

Length of cloth cut so as to make a curtain = 4 m 50 m = 4.50 m

The length of the cloth left with her will be the difference of these two.

Hence, the length of the cloth left with her is
20.05
−4.50
15.55

Therefore, 15.55 m cloth will be remaining.

Page : 182 , Block Name : Exercise 8.6

Page 21 of 22 Aglasem Schools

Book : Mathematics NCERT Solutions | Chapter - 8 Maths

Q6 Namita travels 20 km 50 m every day. Out of this she travels 10 km 200 m by bus and the rest by
auto. How much distance does she travel by auto?

Answer. Total distance travelled by Namita = 20 Km 50 m = 20.050 km

Distance travelled by bus = 10 km 200 m = 10.200 km

Distance travelled by auto = Total distance travelled - Distance travelled by bus
Hence, the distance travelled by auto is
20.050
−10.200
9.850

Page : 182 , Block Name : Exercise 8.6

Q7 Aakash bought vegetables weighing 10 kg. Out of this, 3 kg 500 g is onions, 2 kg 75 g is tomatoes
and the rest is potatoes. What is the weight of the potatoes?

Answer. Total weight of vegetables bought = 10.000 kg

Weight of onions = 3 kg 500 g = 3.500 kg

Weight of tomatoes = 2 kg 75 g = 2.075 kg

Weight of potatoes = Total weight of vegetables bought - (Weight of onions + Weight of tomatoes)

= 10.000 - ( 3.500 + 2.075 )
3.500
−2.075
5.575

Hence, the weight of the potatoes was 4.425 kg
10.000
−5.575
4.425

Page : 182 , Block Name : Exercise 8.6

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