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1.

Write how many centimetres in decimal form.i. 7 cm 1 mmii. 16 mmiii. 144 mmiv. 8 mm

Answer»

i. 7 cm 1 mm

7.1 cm

ii. 16 mm

1.6 cm

iii. 144 mm

14.4 cm

iv. 8 mm

0.8 cm

2.

Read the decimal fraction and write down the place value of each digit:i. 0.59

Answer»

Zero point five nine.

Place value of 5 is 5 x \(\frac{1}{10}=\frac{5}{10}\) = 0.5 and

Place value of 9 is 9 x \(\frac{1}{100}=\frac{9}{100}\) = 0.09

3.

Read the decimal fraction and write down the place value of each digit:12.34

Answer»

Twelve point three four.

Place value of 1 is 1 x 10 = 10

Place value of 2 is 2 x 1 = 2

Place value of 3 is \(3\times\frac{1}{10}\) = 0.3

Place value of 4 is \(4\times\frac{1}{100}\) = 0.04

4.

Read the decimal fraction and write down the place value of each digit:i. 72.05ii. 3.4

Answer»

i. 72.05

Seventy two point zero five

Place value of 7 is 7 x 10 = 70 and of 2 is, it is 2 x 1 = 2

Place value of 5 is 5 x \(\frac{1}{100}=\frac{5}{100}\) = 0.05

ii. 3.4

Three point four.

Place value of 3 is 3 x 1 = 3

Place value of 4 is 4 x \(\frac{1}{10}\) = 0.4

5.

Three strings of lengths 50 m 75 cm; 68 m 58 cm and 121 m 3 cm, respectively, are joined together to get a single string of greatest length, And the length of the single string obtained.If this single string is then divided into 12 equal pieces ; find the length of each piece.

Answer»

1st string 50 m 75 cm = 50.75 m

2nd string 68 m 68 m 58 cm = 68.58 m

3rd string 121 m 3 cm= 121.03 m

On joining three total length = 240.36 m

Now, one string = 240.36 m

Dividing 12 parts = 240.36/12 = 20.3 m.

6.

Read the decimal fraction and write down the place value of each digit:i. 6.13ii. 48.84

Answer»

i. 6.13

Six point one three.

Here 6 is in the units place. 

Hence, its place value is 6 x 1 = 6

1 is in tenths place. 

Hence, its place value is \(1\times\frac{1}{10}=0.1\)

3 is in the hundredths place.

Its place value is 3 x \(\frac{1}{100}\)

= 0.03 100

ii. 48.84

Fourty eight point eight four

Place value of 4 is 4 x 10 = 40 and of 8, it is 8 x 1 = 8

Place value of 8 is 8 x \(\frac{1}{10}=\frac{8}{10}\) = 0.8 and

Place value of 4 is 4 x \(\frac{1}{100}=\frac{4}{100}\) = 0.04

7.

Write how many rupees and how many paise.i. ₹ 58.43ii. ₹ 9.30iii. ₹ 2.30iv. ₹ 2.3

Answer»

i. ₹ 58.43

58 rupees 43 paise.

ii. ₹ 9.30

9 rupees 30 paise.

iii. ₹ 2.30

2 rupees 30 paise.

iv. ₹ 2.3

2 rupees 30 paise.

8.

Evaluate :(i) (3.87 – 2.09) x 2.4(ii) 3.87 x 2.4 – 2.09 x 2.4Are (i) and (ii) equal ?

Answer»

(i) (3.87 – 2.09) x 2.4 = 1.78 x 2.4 = 4.272

(ii) 3.87 x 2.4 – 2.09 x 2.4 = 9.288 – 5.016 = 4.272

Yes, results of (i) and (ii) are equal.

9.

Write the following fractions as decimal fractions.i. Two and a halfii. Two and a quarter

Answer»

i. Two and a half

\(2\frac{1}{2}\) = 2.5 = 2.50

ii. Two and a quarter

\(2\frac{1}{4}\) = 2.25

10.

Write the following fractions as decimal fractions.i. Two and three quartersii. Ten and a halfiii. Fourteen and three quartersiv. Sixteen and a quarterv. Twenty-eight and a half

Answer»

i. Two and three quarters

\(2\frac{3}{4}\) = 2.75

ii. Ten and a half

\(10\frac{1}{2}\) = 10.5 = 10.50

iii. Fourteen and three quarters

\(14\frac{3}{4}\) = 14.75

iv. Sixteen and a quarter

\(16\frac{1}{4}\) = 16.25

v. Twenty-eight and a half

\(28\frac{1}{2}\) = 28.50 = 28.5

11.

Write the following fractions as decimal fractions.i. Thirty and a quarterii. Thirty and a halfiii. Thirty and three quarters

Answer»

i. Thirty and a quarter

\(30\frac{1}{4}\) = 30.25

ii. Thirty and a half

\(30\frac{1}{2}\) = 30.50 = 30.5

iii. Thirty and three quarters

\(30\frac{3}{4}\) = 30.75

12.

Fill in the blanks with 10,100,1000, or 10000 etc.(i) 7.85 x ………….. = 78.5(ii) 0.442 x ………. = 442(iii) 0.0924 x ………… = 9.24(iv) 0.00187 x …………. = 18.7(v) 2.6 x …………. = 2600(vi) 0.08 x ………… = 80(vii) 96.7 ÷ ………….. = 0.967(viii) 5.2 ÷ ……………. = 0.52(ix) 33.15 ÷ ……………….. = 0.03315(x) 0.7 ÷ ………… = 0.007(xi) 0.00672 x ……… = 67.2

Answer»

(i) 7.85 x 10 = 78.5

(ii) 0.442 x 1000 = 442

(iii) 0.0924 x 100 = 9.24

(iv) 0.00187 x 10000 = 18.7

(v) 2.6 x 1000 = 2600

(vi) 0.08 x 1000 = 80

(vii) 96.7 ÷ 100 = 0.967

(viii) 5.2 ÷ 10 = 0.52

(ix) 33.15 ÷ 1000 = 0.03315

(x) 0.7 ÷ 100 = 0.007

(xi) 0.00672 x 10000 = 67.2

13.

Convert the given unlike decimal fractions into like decimal fractions:(i) 1.36, 239.8 and 47.008(ii) 507.0752, 8.52073 and 0.808(iii) 459.22, 7.03093 and 0.200037

Answer»

(i) 1.36 = 1.360

239:8 = 239.800

47.008 = 47.008

(ii) 507.0752 = 507.07520

8.52073 = 8.52073

0.808 = 0.80800

(iii) 459.22 = 459.220000

7.03093 = 7.030930

0.200037 = 0.200037

14.

Write the following mixed fractions in decimal form and read them aloud.i. 5/100ii. 5/10iii. 2/10iv. 20/100

Answer»

i. \(\frac{5}{100}\)

0.05, Zero point zero five.

ii. \(\frac{5}{10}\)

0.5, Zero point five.

iii. \(\frac{2}{10}\)

0.2, Zero point two.

iv. \(\frac{20}{100}\)

0.20, Zero point two zero.

15.

A certain amount of money is distributed among 28 persons. If each person gets Rs. 62.45 and Rs. 5.78 is left, find the original amount of money.

Answer»

Number of persons = 28

Each person gets = RS. 62.45

Total amount distributed to 28 persons = Rs. 62.45 x 28 = Rs. 1748.60

Amount left undistributed = Rs. 5.78

Total amount = Rs. 1748.60 + 5.78 = Rs. 1754.38

16.

By how much should 83.407 be decreased to get 27.78 ?

Answer»

The required number can be formed by subtracting 27.78 from 83.407

Required number = 83.407 – 27.78 = 83.407 – 27.780 = 55.627

17.

The cost of 1 kg of fruit is Rs. 27.50. What is the cost of 3.6 kg of fruit ?

Answer»

Cost of 1 kg fruit = Rs. 27.50

Cost of 3.6 kg fruit = Rs. 27.50 x 3.6 = Rs. 99.00

18.

Simplify :(i) 3.5 – 2.43 + 0.075(ii) 7.84 + 0.3 – 4.016(iii) 2.987 – 1.25 – 0.54(iv) 52.9 – 231.666 + 204

Answer»

(i) 3.5 – 2.43 + 0.075

= 3.500 + 0.075 – 2.43

= 3.575 – 2.430 = 1.145

(ii) 7.84 + 0.3 – 4.016

= 7.840 + 0.300 – 4.016

= 8.140 – 4.016

= 4.124

(iii) 2.987 – 1.25 – 0.54

= 2.987 – 1.79

= 2.987 – 1.790

= 1.197

(iv) 52.9 – 231.666 + 204

= 52.9 – 231.666 + 204.0

= 256.9 – 231.6

= 256.900 – 231.666

= 25.234

19.

Write the following decimal fractions as fractions:1. 0.72. 0.023. 3.85. 0.566. 8.038. 85.49. 147.511. 85.6112. 6.84

Answer»

1. 0.7

7/10

2. 0.02

2/100

3. 3.8

38/10

4. 14.5

145/10

5. 0.56

56/100

6. 8.03

803/100

7. 14.57

1475/10

8. 85.4

854/10

9. 147.5

1475/10

10. 8.5

85/10

11. 85.61

8561/100

12. 6.84

8561/100

20.

Write how many metres in decimal form.i. 110 cm =ii. 60 cm =

Answer»

i. 110 cm = 1.1m

ii. 60 cm = 0.6 m

21.

What number added to 0.805 gives 1 ?

Answer»

The required number will be formed by subtracting 0.805 from 1

Required number = 1 – 0.805 = 1.000 – 0.805 = 0.195

22.

Write how many metres in decimal form.i. 1 m 50 cmii. 50 m 40 cmiii. 50 m 4 cm

Answer»

i. 1 m 50 cm

1.5 m

ii. 50 m 40 cm

50.40 m

iii. 50 m 4 cm

50.04 m

23.

Write how many metres in decimal form.i. 734 cmii. 10 cmiii. 2 cm

Answer»

i. 734 cm

7.34 m

ii. 10 cm

0.1 m

iii. 2 cm

0.02 m

24.

Multiply each of the following numbers by 10, 100 and 1000 :(i) 3.9(ii) 2.89(iii) 0.0829(iv) 40.3(v) 0.3725

Answer»

(i) 3.9 x 10 = 39

3.9 x 100 = 390.0 = 390

3.9 x 1000 = 3900.0 =3900

(ii) 2.89 x 10 = 28.9

2.89 x 100 = 289

2.89 x 1000 = 2890.00 = 2890

(iii) 0.0829 x 10 = 0.829

0.0829 x 100 = 8.29

0.0829 x 1000 = 82.9

(iv) 40.3 x 10 = 403

40.3 x 100 = 4030

40.3 x 1000 = 40300

(v) 0.3725 x 10 = 3.725

0.3725 x 100 = 37.25

0.3725 x 1000 = 372.5

25.

Write how many centimetres and how many millimetres.i. 0.1 cm =ii. 10.5 cm =

Answer»

i. 0.1 cm = 1 mm

ii. 10.5 cm = 10 cm 5 mm

26.

Write how many metres and how many centimetres.i. 58.75 mii. 9.30 miii. 0.30 miv. 0.3 m

Answer»

i. 58.75 m

58 m 75 cm

ii. 9.30 m

9 m 30 cm

iii. 0.30 m

30 cm

iv. 0.3 m

30 cm

27.

Fill in the blanks:1. 8 cm = ......2. 72 cm = ......3. 375 cm = ......4. 4m 80 cm = .......5. 15m. 6 cm = ........

Answer»

1. 8 cm = 0.08 m

1 mm = 100 cm

8cm = 8/100 = 0.08

2. 72 cm = 0.72 m.

1 mm = 100 cm

72 = 72/100 = 0.72

3. 375 cm = 3.75 m.

1 mm = 100 cm

375 cm = 375/100 = 3.75

4. 4m 80 cm = 4.08 m.

1 mm = 100 cm

80cm = 80/100 = 0.8

4m + 0.8m = 4.08 m

5. 15m. 6 cm = 15.06 m.

1 mm = 100 cm

6 cm = 6/100 = 0.06

15m + 0.06 = 15.06m

28.

Fill in the blanks:1. 8mm = .....2. 75 mm = ......3. 8 cm 5 mm = ......4. 525 mm = ........

Answer»

1. 8mm = 0.8 cm

1 cm = 10 mm

8 mm = 8/10 = 0.8 cm

2. 75 mm = 7.5 cm

1 cm = 10 mm

75 mm = 75/10 = 7.5 cm

3. 8 cm 5 mm = 8.5 cm

1 cm = 10 mm

5 mm = 5/10 = 0.5

8 + 0.5 = 8.5 cm+

4. 525 mm = 5.2 cm

1 mm = 10/10

525 mm = 525/10 = 52.5cm

29.

Read the following decimals and write them in words:1. 0.52. 0.133. 1.74. 5.21

Answer»

1. 0.5

Zero point five

2. 0.13

Zero point one three

3. 1.7

One point seven

4. 5.21

Five point two one

30.

Write the numeral representing each of the following:1. Zero point one – two2. Six point eight3. Ten point five4. Four point zero two.5. Six point eight four6. One hundred eight point zero six

Answer»

1. Zero point one – two

0.12

2. Six point eight

6.8

3. Ten point five

10.5

4. Four point zero two.

4.02

5. Six point eight four

6.84

6. One hundred eight point zero six

108.06

31.

The cost of a fountain pen is Rs. 13.25. Find the cost of 8 such pens.

Answer»

Cost of 1 fountain Pen = Rs. 13.25

Cost of 8 fountain Pen = 13.25 x 8 = 106.00 = Rs. 106

32.

If, 317 × 45 = 14265, then 3.17 × 4.5 = ?

Answer»

3.17 × 4.5 

= 14.265

33.

If, 503 × 217 = 109151, then 5.03 × 2.17 = ?

Answer»

5.03 x 2.17 

= 10.9151

34.

The difference between two numbers is 47.364. If the smaller number is 31.855 ; find the bigger one.

Answer»

Difference of two number = 47.364

Smaller number = 31.855

Bigger number = 47.364 + 31.855 = 79.219