NCERT Solutions Class 6 Maths Chapter - 8: Decimals

Exercise 8.1

1. Write the following as numbers in the given table.

(a)

Answer:

Explanation:

Total number of Hundreds = 0

Total number of tens = 3

Total number of ones = 1

Total number of tenths = 2

0 Hundreds + 3 tens + 1 ones + 2 tenths

= 0 × 100 + 3 × 10 + 1 × 1 + 2 × 1/10

= 0 + 30 + 1 + 0.2

= 31.2

(b)

Answer:

Explanation:

Total number of Hundreds = 1

Total number of tens = 1

Total number of ones = 0

Total number of tenths = 4

1 Hundreds + 1 tens + 0 ones + 4 tenths

= 1 × 100 + 1 × 10 + 0 × 1 + 4 × 1/10

= 100 + 10 + 0 + 0.4

= 110.4

2. Write the following decimals in the place value table.

1. 19.4
2. 0.3
3. 10.6
4. 205.9

Answer:

Explanation:

(a.) 19.4

19. 4 = 10 + 9 + 0.4

= 1 × 10 + 9 × 1 + 4 × 1/10

= 1 × Tens + 9 × Ones + 4 × Tenths

Since there are no hundreds, so hundred = 0.

(b.) 0.3

0.3 = 3 × 1/10

= 3 × Tenths

(c.) 10.6

10.6 = 10 + 0.6

= 1 × 10 + 6 × 1/10

= 1 × Tens + 6 × Tenths

Since there are no hundreds and ones, so hundred = 0, Ones = 0.

(d.) 205.9

205.9 = 200 + 5 + 0.9

= 2 × 100 + 5 × 1 + 9 × 1/10

= 2 × Hundreds + 5 × Ones + 9 × Tenths

Since there are no tens and ones, so tens = 0.

3. Write each of the following as decimals:

(a) Seven-tenths

Answer: 0.7

Explanation: Seven tenths = 7 × 1/10

= 0.7

(b) Two tens and nine-tenths

Answer: 20.9

Explanation: 2

(c) Fourteen point six

Answer: 14.6

Explanation: 14 + 6 × 1/10

= 14 + 0.6

= 14.6

(d) One hundred and two ones

Answer: 102.0

Explanation: One hundred + two ones

= 1 × 100 + 2 × 1

= 100 + 2

= 102

Since there are no tenths, so place after decimal will be 0

(e) Six hundred point eight

Answer: 600.8

Explanation: 6 × 100 + 8 × 1/10

= 600 + 0.8

= 600.8

4. Write each of the following as decimals:

(a) 5/10

Answer: 0.5

Explanation: 5/10

= 5 tenths

= 0.5

(b) 3 + 7/10

Answer: 3.7

Explanation: 3 Ones + 7 Tenths

= 3 × 1 + 7 × 1/10

= 3 + 0.7

= 3.7

(c) 200 + 60 + 5 + 1/10

Answer: 265.1

Explanation: 2 Hundreds + 6 Tens + 5 Ones + 1 Tenths

= 2 × 100 + 6 × 10 + 5 × 1 + 1 × 1/10

= 200 + 60 + 5 + 0.1

265.1

(d) 70 + 8/10

Answer: 70.8

Explanation: 7 tens + 8 Tenths

= 7 × 10 + 8 × 1/10

= 70 + 0.8

= 70.8

(e) 88/10

Answer: 8.8

Explanation: 8 Ones + 8 Tenths

= 8.8

(f) 42/10

Answer: 4.2

Explanation: 42/10

= 4.2

(g) 3/2

Answer: 1.5

Explanation: Multiply the fraction by 5,

(3 × 5)/ (2 × 5)

= 15/10

= 15 tenths

= 15 × 1/10

= 1.5

(h) 2/5

Answer: 0.4

Explanation: Multiply the fraction by 2,

(2 × 2)/ (5 × 2)

= 4/10

= 4 × 1/10

= 0.4

(i) 12/5

Answer: 2.4

Explanation: Multiply the fraction by 2,

(12 × 2)/ (5 × 2)

= 24/10

= 24 × 1/10

= 2.4

(j) 3 3/5

Answer: 3.6

Explanation: 3 + 3/5

Let's multiply the fraction (3/5) by 2,

3 + (3 × 2)/ (5 × 2)

= 3 + 6/10

= 3 + 0.6

= 3.6

(k) 4 1/2

Answer: 4.5

Explanation: 4 + 1/2

Let's multiply the fraction (1/2) by 5,

= 4 + (1 × 5)/ (2 × 5)

= 4 + 5/10

= 4 + 0.5

= 4.5

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

(a) 0.6

Answer: 6/10 or 3/5

Explanation: 0.6 = 6/10

Both 6 and 10 have a common factor 2. Let's divide the numerator and the denominator by 2 to convert the fraction to its lowest form.

(2 × 3)/ (2 × 5)

= 3/5

(b) 2.5

Answer: 25/10 or 5/2

Explanation:

2.5 = 25/10

Both 25 and 10 have a common factor 5. Let's divide the numerator and the denominator by 5 to convert the fraction to its lowest form.

(5 × 5)/ (2 × 5)

= 5/2

(c) 1.0

Answer: 1

Explanation: 1.0

= 10/10

= 1

(d) 3.8

Answer: 38/10 or 19/5

Explanation:

= 38/10

Both 38 and 10 have a common factor 2. Let's divide the numerator and the denominator by 2 to convert the fraction to its lowest form.

(2 × 19 (2 × 5)

= 19/5

(e) 13.7

Answer: 137/10

Explanation: 13.7 = 137/10

The numerator and the denominator do not have any factor in common. It is already present in its lowest form.

(f) 21.2

Answer: 212/10 or 106/5

Explanation:

= 212/10

Both 212 and 10 have a common factor 2. Let's divide the numerator and the denominator by 2 to convert the fraction to its lowest form.

(2 × 106)/ (2 × 5)

= 106/5

(g) 6.4

Answer: 64/10 or 32/5

Explanation:

6.4 = 64/10

Both 64 and 10 have a common factor 2. Let's divide the numerator and the denominator by 2 to convert the fraction to its lowest form.

(2 × 32)/ (2 × 5)

= 32/5

6. Express the following as cm using decimals.

1m = 100 cm

1 cm = 1/100 m

1 cm = 0.01 m

1 cm = 10 mm

1mm = 1/10 cm

1 mm = 0.1 cm

(a) 2 mm

Answer: 0.2 cm

Explanation: 1mm = 1/10 cm

2 mm = 2 × 1/10 cm

= 0.2 cm

(b) 30 mm

Answer: 3.0 cm

Explanation: 1mm = 1/10 cm

30 mm = 30 × 1/10 cm

= 30/10 cm

= 3.0 cm

(c) 116 mm

Answer: 11.6 cm

Explanation: 1mm = 1/10 cm

116 mm = 116 × 1/10 cm

= 116/10 cm

= 11.6 cm

(d) 4 cm 2 mm

Answer: 4.2 cm

Explanation: 1mm = 1/10 cm

4 cm + 2 × 1/10 cm

= 4 + 0.2

= 4.2 cm

(e) 162 mm

Answer: 16.2 cm

Explanation: 1mm = 1/10 cm

162 mm = 162 × 1/10 cm

= 16.2 cm

(f)83 mm

Answer: 8.3 cm

Explanation: 1mm = 1/10 cm

83 mm = 83 × 1/10 cm

= 83/10 cm

= 8.3 cm

7. 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

Answer: 0 and 1; 1

Explanation: 0.8 lies between 0 and 1.

0.8 is nearer to the number 1.

(b) 5.1

Answer: 5 and 6; 5

Explanation: 5.1 lie between 5 and 6.

The number 5.1 is nearer to the number 5.

(c) 2.6

Answer: 2 and 3; 3

Explanation: 2.6 lie between 2 and 3.

The number 2.6 is nearer to the number 3.

(d) 6.4

Answer: 6 and 7; 6

Explanation: 6.4 lie between 7 and 6.

The number 6.4 is nearer to the number 6.

(e) 9.1

Answer: 9 and 10; 9

Explanation: 9.1 lie between 9 and 10.

The number 9.1 is nearer to the number 9.

(f) 4.9

Answer: 4 and 5; 5

Explanation: 4.9 lie between 4 and 5.

The number 4.9 is nearer to the number 5.

8. Show the following numbers on the number line.

(a) 0.2

(b) 1.9

(c) 1.1

(d) 2.5

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

Answer:

A = 0.8

B = 1.3

C = 2.2

D = 2.9

10.

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

Answer: 9.5 cm

9 cm 5 mm = 9 cm + 5 × 1/10 cm

= 9 cm + 5/10 cm

= (9 + 0.5) cm

= 9.5 cm

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

Answer: 6.5 cm

65 mm = 65 × 1/10 cm

= 65/10 cm

= 6.5 cm

Exercise 8.2

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

Answer:

Explanation:

(a) 0 Ones + 2 Tenths + 6 Hundredths

= 0 × 1 + 2 × 1/10 + 6 × 1/100

= 0 + 2/10 + 6/100

= 0 + 0.2 + 0.06

= 0.26

(b) 1 Ones + 3 Tenths + 8 Hundredths

= 1 × 1 + 3 × 1/10 + 8 × 1/100

= 1 + 3/10 + 8/100

= 1 + 0.3 + 0.08

= 1.38

(c) 1 Ones + 2 Tenths + 8 Hundredths

= 1 × 1 + 2 × 1/10 + 8 × 1/100

= 1 + 2/10 + 8/100

= 1 + 0.2 + 0.08

= 1.28

2. Write the numbers given in the following place value table in decimal form.

(a)

Answer: 3.25

Explanation:

0 Hundreds + 0 Tens + 3 Ones + 2 Tenths + 5 Hundredths + 0 Thousandths

= 0 × 100 + 0 × 10 + 3 × 1 + 2 × 1/10 + 5 × 1/100 + 0 × 1/1000

= 0 + 0 + 3 + 2/10 + 5/100 + 0

= 3 + 0.2 + 0.05

= 3.25

(b)

Answer: 102.63

Explanation:

1 Hundreds + 0 Tens + 2 Ones + 6 Tenths + 3 Hundredths + 0 Thousandths

= 1 × 100 + 0 × 10 + 2 × 1 + 6 × 1/10 + 3 × 1/100 + 0 × 1/1000

= 100 + 0 + 2 + 6/10 + 3/100 + 0

= 100 + 2 + 0.6 + 0.03

= 102.63

(c)

Answer: 30.025

Explanation:

0 Hundreds + 3 Tens + 0 Ones + 0 Tenths + 2 Hundredths + 5 Thousandths

= 0 × 100 + 3 × 10 + 0 × 1 + 0 × 1/10 + 2 × 1/100 + 5 × 1/1000

= 0 + 30 + 0 + 0 + 2/100 + 5/1000

= 30 + 0.02 + 0.005

= 30.025

(d)

Answer: 211.902

Explanation:

2 Hundreds + 1 Tens + 1 Ones + 9 Tenths + 0 Hundredths + 2 Thousandths

= 2 × 100 + 1 × 10 + 1 × 1 + 9 × 1/10 + 0 × 1/100 + 2 × 1/1000

= 200 + 10 + 1 + 9/10 + 0 + 2/1000

= 211 + 0.9 + 0.002

= 211.902

(e)

Answer: 12.241

Explanation:

0 Hundreds + 1 Tens + 2 Ones + 2 Tenths + 4 Hundredths + 1 Thousandths

= 0 × 100 + 1 × 10 + 2 × 1 + 2 × 1/10 + 4 × 1/100 + 1 × 1/1000

= 0 + 10 + 2 + 2/10 + 4/100 + 1/1000

= 12 + 0.2 + 0.04 + 0.001

= 12.241

3. Write the following decimals in the place value table.

1. 0.29
2. 2.08
3. 19.60
4. 148.32
5. 200.812

Answer: The decimal values in the place value table are shown below:

4. Write each of the following as decimals.

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

Answer: 29.41

Explanation:

20 + 9 + 4/10 + 1/100

= 20 + 9 + 0.4 + 0.01

= 29.41

(b) 137 + 5/100

Answer: 137.05

Explanation:

137 + 0.05

= 137.05

(c) 7/10 + 6/100 + 4/1000

Answer: 0.764

Explanation:

0.7 + 0.06 + 0.004

= 0.764

(d) 23 + 2/10 + 6/1000

Answer: 23.206

Explanation: 23 + 0.2 + 0.006

23.206

(e) 700 + 20 + 5 + 9/100

Answer: 725.09

Explanation: 700 + 20 + 5 + 0.09

= 725.09

5. Write each of the following decimals in words.

(a) 0.03

Answer: Zero point zero three

(b) 1.20

Answer: One point two zero

(c) 108.56

Answer: One hundred eight point five six

(d) 10.07

Answer: Ten point zero seven

(e) 0.032

Answer: Zero point zero three two

(f) 5.008

Answer: Five point zero zero eight

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

(a) 0.06

Answer: 0 and 0.1

(b) 0.45

Answer: 0.4 and 0.5

(c) 0.19

Answer: 0.1 and 0.2

(d) 0.66

Answer: 0.6 and 0.7

(e) 0.92

Answer: 0.9 and 1.0

(f) 0.57

Answer: 0.5 and 0.6

7. Write as fractions in lowest terms.

Lowest refers to the value of a fraction where the numerator and the denominator has only 1 as the common factor.

(a) 0.60

Answer: 3/5

Explanation: 0.60 = 60/100

Factors of 60 = 2 × 2 × 3 × 5

Factors of 100 = 2 × 2 × 5 × 5

Dividing the fraction by the common factors = 2 × 2 × 5 = 20

= 3/5

(b) 0.05

Answer: 1/20

Explanation:

0.05 = 5/100

Dividing the fraction by 5, we get:

1/20

(c) 0.75

Answer: 3/4

Explanation: 0.75 = 75/100

Dividing the fraction by 25, we get:

(25 × 3)/ (25 × 4)

= 3/4

(d) 0.18

Answer: 9/50

Explanation: 0.18 = 18/100

Dividing the fraction by 2, we get:

(2 × 9)/ (2 × 50)

= 9/50

(e) 0.25

Answer: 1/4

Explanation: 0.25 = 25/100

Dividing the fraction by 25, we get:

(25 × 1)/ (25 × 4)

= 1/4

(f) 0.125

Answer: 1/8

Explanation: 0.125 = 125/100

Dividing the fraction by 125, we get:

(125 × 1)/ (125 × 8)

= 1/8

(g) 0.066

Answer: 33/500

Explanation: 0.066 = 66/1000

Dividing the fraction by 2, we get:

(2 × 33)/ (2 × 500)

= 33/500

Exercise 8.3

1. Which is greater?

(a) 0.3 or 0.4

Answer: 0.4

Explanation: 0.4 > 0.3

4/10 > 3/10

(b) 0.07 or 0.02

Answer: 0.07

Explanation:

0.07 > 0.02

7/100 > 2/100

(c) 3 or 0.8

Answer: 3 > 0.8

Explanation:

3 > 0.8

The decimal value (0.8) is less than the whole number 3.

(d) 0.5 or 0.05

Answer: 0.5 > 0.005

Explanation:

5/10 > 5/100

1/10 is greater than 1/100.

(e) 1.23 or 1.2

Answer: 1.23 > 1.2

Explanation:

Multiply both numbers by 100.

2.23 × 100 > 1.2 × 100

123 > 120

Hence, 1.23 is greater than 1.2.

(f) 0.099 or 0.19

Answer: 0.19

Explanation:

Multiply both the numbers by 1000.

0.099 × 1000 = 99

0.19 × 1000 = 190

Thus,

190 > 99

0.19 > 0.099

Or

0.099 < 0.19

(g) 1.5 or 1.50

Answer: Both are the same

Explanation:

Let's multiply both the numbers by 100.

1.5 × 100 = 150

1.50 × 100 = 150

Thus,

1.5 = 1.50

The zero after the decimal value does not change the value of the number.

For example,

2.0 = 2

2.22 = 2.2200

(h) 1.431 or 1.490

Answer: 1.490

Explanation: Let's multiply both the numbers by 1000.

1.431 × 1000 = 1431

1.490 × 1000 = 1490

Thus,

1431 < 1490

Or

1.431 < 1.490

(i) 3.3 or 3.300

Answer: Both are equal

Explanation: 3.3 = 3.300

The zero after the decimal value does not change the value of the number.

For example,

4.55 = 4.5500

2.0 = 2.000

(j) 5.64 or 5.603

Answer: 5.64

Explanation: Let's multiply both the numbers by 1000.

5.64 × 1000 = 5640

5.603 × 1000 = 5603

Thus,

5640 > 5603

5.64 > 5.603

2. Make five more examples and find the greater number from them.

The five examples are given below:

1. 0.2 < 0.6
2. 0.20 > 0.020
3. 0.5 < 0.9
4. 4.4 < 6.4
5. 2.00 > 0.20

Exercise 8.4

1. Express as rupees using decimals.

1 rupee = 100 paisa

1 paisa = 1/100 rupee

1 paisa = 0.01 rupee

(a) 5 paise

Answer: 0.05 rupee

Explanation: 1 paisa = 0.01 rupee

5 paisa = 5 × 0.01

= 0.05 rupee

(b) 75 paise

Answer: 0.75 rupee

Explanation: 1 paisa = 0.01 rupee

75 paisa = 75 × 0.01

= 0.75 rupee

(c) 20 paise

Answer: 0.20 rupee

Explanation: 1 paisa = 0.01 rupee

20 paisa = 20 × 0.01

= 0.20 rupee

(d) 50 rupees 90 paise

Answer: 50.90 rupee

Explanation: 1 paisa = 0.01 rupee

90 piasa = 90 × 0.01

= 0.90 rupee

50 rupee + 0.90 rupee

= 50.90 rupee

(e) 725 paise

Answer: 7.25 rupee

Explanation: 1 paisa = 0.01 rupee

725 paisa = 725 × 0.01

= 7.25 rupee

= 7 rupee and 0.25 paisa

2. Express as metres using decimals.

1m = 100 cm

1 cm = 1/100 m

1 cm = 0.01 m

(a) 15 cm

Answer: 0.15 m

Explanation: 1m = 100 cm

1 cm = 0.01 m

15 cm = 15 × 0.01 m

= 0.15 m

(b) 6 cm

Answer: 0.06 m

Explanation: 1m = 100 cm

1 cm = 0.01 m

6 cm = 6 × 0.01 m

= 0.06 m

(c) 2 m 45 cm

Answer: 2.45 m

Explanation: 1m = 100 cm

1 cm = 0.01 m

45 cm = 45 × 0.01 m

= 0.45 m

2 m + 45 cm

= 2 m + 0.45 m

= 2.45 m

(d) 9 m 7 cm

Answer: 9.07 m

Explanation: 1m = 100 cm

1 cm = 0.01 m

7 cm = 7 × 0.01 m

= 0.07 m

9m 7 cm

= 9 m + 0.07 m

= 9.07 m

(e) 419 cm

Answer: 4.19 m

Explanation: 1m = 100 cm

1 cm = 0.01 m

419 cm = 419 × 0.01 m

= 4.19 m

= 4 m and 19 cm

3. Express as cm using decimals.

1 cm = 10 mm

1 mm = 1/10 cm

1 mm = 0.1 cm

(a) 5 mm

Answer: 0.5 cm

Explanation: 1 cm = 10 mm

1 mm = 0.1 cm

5 mm = 0.1 × 5

= 0.5 cm

(b) 60 mm

Answer: 6.0 cm

Explanation: 1 cm = 10 mm

1 mm = 0.1 cm

60 mm = 0.1 × 60

= 6.0 cm

(c) 164 mm

Answer: 16.4 cm

Explanation: 1 cm = 10 mm

1 mm = 0.1 cm

164 mm = 0.1 × 164

= 16.4 cm

(d) 9 cm 8 mm

Answer: 9.8 cm

Explanation: 1 cm = 10 mm

1 mm = 0.1 cm

8 mm = 0.1 × 8

= 0.8 cm

9 cm + 0.8 cm

= 9.8 cm

(e) 93 mm

Answer: 9.3 cm

Explanation: 1 cm = 10 mm

1 mm = 0.1 cm

93 mm = 0.1 × 93

= 9.3 cm

4. Express as km using decimals.

1 km = 1000m

1 m = 1/1000 km

1m = 0.001 km

(a) 8 m

Answer: 0.008 km

Explanation: 1 km = 1000m

1m = 0.001 km

8 m = 0.001 × 8

= 0.008 km

(b) 88 m

Answer: 0.088 km

Explanation: 1 km = 1000m

1m = 0.001 km

88 m = 0.001 × 88

= 0.088 km

(c) 8888 m

Answer: 8.888 km

Explanation: 1 km = 1000m

1m = 0.001 km

8888 m = 0.001 × 8888

= 8.888 km

(d) 70 km 5 m

Answer: 70.005 km

Explanation: 1 km = 1000m

1m = 0.001 km

5 m = 0.001 × 5

= 0.005 km

70 km 5 m

= 70 km + 0.005 km

= 70.005 km

5. Express as kg using decimals.

1 kg = 1000 g

1 g = 1/1000 kg

1g = 0.0001 kg

(a) 2 g

Answer: 0.002 kg

Explanation: 1 kg = 1000 g

1g = 0.0001 kg

2 g = 0.001 × 2

= 0.002 kg

(b) 100 g

Answer: 0.1 kg

Explanation: 1 kg = 1000 g

1g = 0.0001 kg

100 g = 0.001 × 100

= 0.1 kg

(c) 3750 g

Answer: 3.750 kg

Explanation: 1 kg = 1000 g

1g = 0.0001 kg

3750 g = 0.001 × 3750

= 3.750 kg

= 3.75 kg

(d) 5 kg 8 g

Answer: 5.008 kg

Explanation: 1 kg = 1000 g

1g = 0.0001 kg

8 g = 0.001 × 8

= 0.008 kg

5 kg 8 g

= 5 kg + 0.008 kg

= 5.008 kg

(e) 26 kg 50 g

Answer: 26.05 kg

Explanation: 1 kg = 1000 g

1g = 0.0001 kg

50 g = 0.001 × 50

= 0.05 kg

26 kg 50 g

= 26 kg + 0.05 kg

= 26.05 kg

Exercise 8.5

1. Find the sum in each of the following:

(a) 0.007 + 8.5 + 30.08

Answer: 38.587

(b) 15 + 0.632 + 13.8

Answer: 29.432

(c) 27.076 + 0.55 + 0.004

Answer: 27.630

(d) 25.65 + 9.005 + 3.7

Answer: 38.355

(e) 0.75 + 10.425 + 2

Answer: 13.175

(f) 280.69 + 25.2 + 38

Answer: 343.89

2. Rashid spent rupees 35.75 for Maths book and rupees 32.60 for Science book. Find the total amount spent by Rashid.

Answer: Rupees 68.35

Total rupees spent by Rashid for Maths book = 35.75

Total rupees spent by Rashid for Science book = 32.60

Total amount spent by Rashid = Rupees spent for Maths book + Rupees spent for Science book

Total amount spent by Rashid = 35.75 + 32.60

= 68.35

Thus, the total amount spent by Rashid is rupees 68.35.

3. Radhika's mother gave her rupees 10.50 and her father gave her rupees 15.80, find the total amount given to Radhika by the parents.

Answer: Rupees 26.30

Rupees given to Radhika by her mother = 10.50

Rupees given to Radhika by her father = 15.80

Total amount = 10.50 + 15.80

= 26.30

Thus, the total amount given to Radhika by her parents is 26.30 rupees.

4. 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: 5m 25 cm or 5.25 m

Cloth bought by Nasreen for her skirt = 3 m 20 cm

Cloth bought by Nasreen for her trouser = 2 m 5 cm

Total length of cloth = 3 m 20 cm + 2 m 5 cm

= 5m 25 cm

Thus, the total length of cloth bought by Nasreen is equal to 5.25 m.

5. 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: 3.042 km

Distance walked by Naresh in the morning = 2 km 35 m

Distance walked by Naresh in the evening = 1 km 7 m

Total distance = 2 km 35 m + 1 km 7 m

= 3 km 42 m

1 km = 1000 m

1m = 1/1000 km

42 m = 42/1000

= 0.042 km

3 km + 0.042 km = 3.042 km

Thus, the total distance walked by Naresh is 3.042 km.

6. 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: 22.775 km

Distance travelled by Sunita by bus = 15 km 268 m

Distance travelled by Sunita by car = 7 km 7 m

Distance travelled by Sunita on foot = 500 m

Total distance = 15 km 268 m + 7 km 7 m + 500 m

= (15 + 7) km (268 + 7 + 500) m

= 22 km 775m

575 m = 0.775 km

Total distance = 22 km + 0.775 km

= 22.775 km

Thus, Sunita's school is 22.775 km far from her residence.

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

Answer: 18.270 kg

Weight of rice purchased by Ravi = 5 kg 400 g

Weight of sugar purchased by Ravi = 2 kg 20 g

Weight of flour purchased by Ravi = 10 kg 850g

Total weight = 5 kg 400 g + 2 kg 20 g + 10 kg 850g

= (5 + 2 + 10) kg (400 + 20 + 850)g

= 17 kg 1270 g

1 kg = 1000 g

1270 g = 1.270 kg

Total weight = 17 kg + 1.270 kg

= 18.270 kg

Thus, the total weight of his purchases is 18.270 kg.

Exercise 8.6

1. Subtract:

(a) 18.25 from 20.75

Answer:

20.75 - 18.25

= 1.75

(b) 202.54 m from 250 m

Answer:

250 - 202.54

= 250.00 m - 202.54 m

= 47.46 m

(c) 5.36 from 8.40

Answer:

8.40 - 5.36

= 3.04

(d) 2.051 km from 5.206 km

Answer:

5.206 km - 2.051 km

= 3.155 km

(e) 0.314 kg from 2.107 kg

Answer:

2.107 kg - 0.314 kg

= 1.793 kg

2. Find the value of:

(a) 9.756 - 6.28

Answer: 3.476

(b) 21.05 - 15.27

Answer: 5.78

(c) 18.5 - 6.79

Answer: 11.71

(d) 11.6 - 9.847

Answer: 1.753

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

Answer: Rupees 14.35

Price of a book bought by Raju = 35.65

Amount given to the shopkeeper = 50

Money left = 50 - 35.65

= 14.35

Thus, Raju got rupees 14.35 back from the shopkeeper.

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

Answer: Rupees 6.75

Price of ice-cream bought by Rani = 11.75

Total amount with Rani = 18.50

Amount left = 18.50 - 11.75

= 6.75

Thus, Rani have rupees 6.27 left with her.

5. 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: 15.55 m

Total length of the cloth = 20 m 5 cm

= 20.05 m

(1 m = 100 cm)

Length of the cut out cloth to make a curtain = 4 m 50 cm

= 4.50 m

Cloth left = 20.05 m - 4.50 m

= 15.55 m

Thus, 15.55 m of cloth was left with Tina.

6. 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:

Distance travelled by Namita everyday = 20 km 50 m

Distance travelled by Namita by bus = 10 km 200 m

Distance travelled by Namita by auto = Total distance - Distance by bus

= 20 km 50 m - 10 km 200 m

= 20.050 km - 10.200 km

(1 km = 1000m)

= 9.850 km

7. 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: 4.425 kg

Weight of vegetables bought by Aakash = 10 kg

Weight of onions = 3 kg 500 g

= 3.5 kg or 3.500 kg

Weight of tomatoes = 2 kg 75 g

= 2.075 kg

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

= 10 kg - (3.500 kg + 2.075 kg)

= 10 kg - 5.575 kg

= 4.425 kg

Thus, the total weight of the potatoes is 4.425 kg.