Selina Solutions Concise Maths Class 7 Chapter 4 Decimal Fractions (Decimals) help students understand the basic concepts covered in this chapter. Students can solve the exercise wise problems by using the solutions designed by faculty at BYJUâ€™S. The solutions are created, keeping in mind the understanding capacity of students. Selina Solutions Concise Maths Class 7 Chapter 4 Decimal Fractions (Decimals), PDF links are given here.

Chapter 4 explains concepts like converting decimal fraction into a fraction and vice versa, decimal places and various mathematical operations on them. Students can refer to the PDF of solutions and solve textbook problems, without any time constraints.

## Selina Solutions Concise Maths Class 7 Chapter 4: Decimal Fractions (Decimals) Download PDF

### Exercises of Selina Solutions Concise Maths Class 7 Chapter 4 – Decimal Fractions (Decimals)

## Access Selina Solutions Concise Maths Class 7 Chapter 4: Decimal Fractions (Decimals)

#### Exercise 4A page: 57

**1. Convert the following into fractions in their lowest terms:**

**(i) 3.75**

**(ii) 0.5**

**(iii) 2.04**

**(iv) 0.65**

**(v) 2.405**

**(vi) 0.085**

**(vii) 8.025**

**Solution:**

(i) 3.75

We can write it as

= 375/ 100

Here the HCF of 375 and 100 is 25

= (375 Ã· 25)/ (100 Ã· 25)

So we get

= 15/4

(ii) 0.5

We can write it as

= 5/10

= 1/2

(iii) 2.04

We can write it as

= 204/100

Here the HCF of 204 and 100 is 4

= (204 Ã· 4)/ (100 Ã· 4)

So we get

= 51/25

(iv) 0.65

We can write it as

= 65/100

Here the HCF of 65 and 100 is 5

= (65 Ã· 5)/ (100 Ã· 5)

So we get

= 13/20

(v) 2.405

We can write it as

= 2405/1000

Here the HCF of 2405 and 1000 is 5

= (2405 Ã· 5)/ (1000 Ã· 5)

So we get

= 481/200

(vi) 0.085

We can write it as

= 85/1000

Here the HCF of 85 and 1000 is 5

= (85 Ã· 5)/ (1000 Ã· 5)

So we get

= 17/200

(vii) 8.025

We can write it as

= 8025/1000

Here the HCF of 8025 and 1000 is 25

= (8025 Ã· 25)/ (1000 Ã· 25)

So we get

= 321/ 40

**2. Convert into decimal fractions:**

**(i) 2 4/5**

**(ii) 79/100**

**(iii) 37/10,000**

**(iv) 7543/10 ^{4}**

**(v) 3/4 **

**(vi) 9 3/5**

**(vii) 8 5/8**

**(viii) 5 7/8**

**Solution:**

(i) 2 4/5

We can write it as

= 14/5 Ã— 2/2

So we get

= 28/10

= 2.8

(ii) 79/100

We can write it as

= 79/100

= 0.79

(iii) 37/10,000

We can write it as

= 37/10,000

= 0.0037

(iv) 7543/10^{4}

We can write it as

= 7543/10000

= 0.7543

(v) 3/4

By division we get

= 0.75

(vi) 9 3/5

We can write it as

= 48/5

By division

So we get

= 9.6

(vii) 8 5/8

By division we get

= 8.625

(viii) 5 7/8

By division we get

= 5.875

**3. Write the number of decimal places in:**

**(i) 0.4762**

**(ii) 7.00349**

**(iii) 8235.403**

**(iv) 35.4**

**(v) 2.608**

**(vi) 0.000879**

**Solution:**

(i) 0.4762

There are four decimal places.

(ii) 7.00349

There are five decimal places.

(iii) 8235.403

There are three decimal places.

(iv) 35.4

There is one decimal place.

(v) 2.608

There are three decimal places.

(vi) 0.000879

There are six decimal places.

**4. Write the following decimals as word statements:**

**(i) 0.4, 0.9, 0.1**

**(ii) 1.9, 4.4, 7.5**

**(iii) 0.02, 0.56, 13.06**

**(iv) 0.005, 0.207, 111.519**

**(v) 0.8, 0.08, 0.008, 0.0008**

**(vi) 256.1, 10.22, 0.634**

**Solution:**

(i) 0.4 = zero-point-four

0.9 = zero-point-nine

0.1 = zero-point-one

(ii) 1.9 = one-point-nine

4.4 = four-point-four

7.5 = seven-point-five

(iii) 0.02 = zero-point-zero-two

0.56 = zero-point-five-six

13.06 = thirteen-point-zero-six

(iv) 0.005 = zero-point-zero-zero-five

0.207 = zero-point-two-zero-seven

111.519 = one hundred eleven-point-five-one-nine

(v) 0.8 = zero-point-eight

0.08 = zero-point-zero-eight

0.008 = zero-point-zero-zero-eight

0.0008 = zero-point-zero-zero-zero-eight

(vi) 256.1 = two hundred fifty six-point-one

10.22 = ten-point-two-two

0.634 = zero-point-six-three-four

**5. Convert the given fractions into like fractions:**

**(i) 0.5, 3.62, 43.981 and 232.0037**

**(ii) 215.78, 33.0006, 530.3 and 0.03569**

**Solution:**

(i) 0.5, 3.62, 43.981 and 232.0037

The greatest decimal places is 4

So we get

0.5 = 0.5000

3.62 = 3.6200

43.981 = 43.9810

232.0037 = 232.0037

(ii) 215.78, 33.0006, 530.3 and 0.03569

The greatest decimal places is 5

215.78 = 215.78000

33.0006 = 33.00060

530.3 = 530.30000

0.03569 = 0.03569

#### Exercise 4B page: 59

**1. Add: **

**(i) 0.5 and 0.37 **

**(ii) 3.8 and 8.7**

**(iii) 0.02, 0.008 and 0.309**

**(iv) 0. 4136, 0. 3195 and 0.52**

**(v) 9.25, 3.4 and 6.666**

**(vi) 3.007, 0.587 and 18.341**

**(vii) 0.2, 0.02 and 2.0002**

**(viii) 6. 08, 60.8, 0.608 and 0.0608**

**(ix) 29.03, 0.0003, 0.3 and 7.2**

**(x) 3.4, 2.025, 9.36 and 3.6221**

**Solution:**

**(i) 0.5 and 0.37 **

**So we get**

**0.5 + 0.37 = 0.87**

**(ii) 3.8 and 8.7**

**So we get**

**3.8 + 8.7 = 12.5**

**(iii) 0.02, 0.008 and 0.309**

**So we get**

**0.02 + 0.008 + 0.309 = 0.337**

**(iv) 0.4136, 0.3195 and 0.52**

**So we get**

**0.4136 + 0.3195 + 0.52 = 1.2531**

**(v) 9.25, 3.4 and 6.666**

**So we get**

**9.25 + 3.4 + 6.666 = 19.316**

**(vi) 3.007, 0.587 and 18.341**

**So we get**

**3.007 + 0.587 + 18.341 = 21.935**

**(vii) 0.2, 0.02 and 2.0002**

**So we get**

**0.2 + 0.02 + 2.0002 = 2.2202**

**(viii) 6.08, 60.8, 0.608 and 0.0608**

**So we get**

**6.08 + 60.8 + 0.608 + 0.0608 = 67.5488**

**(ix) 29.03, 0.0003, 0.3 and 7.2**

**So we get**

**29.03 + 0.0003 + 0.3 + 7.2 = 36.5303**

**(x) 3.4, 2.025, 9.36 and 3.6221**

**So we get**

**3.4 + 2.025 + 9.36 + 3.6221 = 18.4071**

**2. Subtract the first number from the second: (i) 5.4, 9.8(ii) 0.16, 4.3(iii) 0.82, 8.6(v) 2.237, 9.425(vi) 41 .03, 59.46(vii) 3.92. 26.86(viii) 4.73, 8.5(ix) 12.63, 36.2(x) 0.845, 3.71**

**Solution:**

**(i) 5.4, 9.8It can be written as**

**9.8 â€“ 5.4 = 4.4**

**(ii) 0.16, 4.3It can be written as**

**4.3 â€“ 0.16 = 4.14**

**(iii) 0.82, 8.6It can be written as**

**8.6 â€“ 0.82 = 7.78**

**(v) 2.237, 9.425It can be written as**

**9.425 â€“ 2.237 = 7.188**

**(vi) 41 .03, 59.46It can be written as**

**59.46 â€“ 41.03 = 18.43**

**(vii) 3.92, 26.86It can be written as**

**26.86 â€“ 3.92 = 22.94**

**(viii) 4.73, 8.5It can be written as**

**8.5 â€“ 4.73 = 3.77**

**(ix) 12.63, 36.2It can be written as**

**36.2 â€“ 12.63 = 23.57**

**(x) 0.845, 3.71**

It can be written as

3.71 â€“ 0.845 = 2.865

**3. Simplify: (i) 28.796 -13.42 â€“ 2.555(ii) 93.354 â€“ 62.82 â€“ 13.045(iii) 36 â€“ 18.59 â€“ 3.2(iv) 86 + 16.95 â€“ 3.0042(v) 32.8 â€“ 13 â€“ 10.725 +3.517(vi) 4000 â€“ 30.51 â€“ 753.101 â€“ 69.43(vii) 0.1835 + 163.2005 â€“ 25.9 â€“ 100(viii) 38.00 â€“ 30 + 200.200 â€“ 0.230(ix) 555.555 + 55.555 â€“ 5.55 â€“ 0.555**

**Solution:**

**(i) 28.796 -13.42 â€“ 2.555It can be written as**

**= 28.796 â€“ (13.42 + 2.555) **

**On further calculation**

**= 28.796 â€“ 15.975**

**= 12.821**

**(ii) 93.354 â€“ 62.82 â€“ 13.045It can be written as**

**= 93.354 â€“ (62.82 + 13.045)**

**On further calculation**

**= 93.354 â€“ 75.865**

**= 17.489**

**(iii) 36 â€“ 18.59 â€“ 3.2It can be written as**

**= 36 â€“ (18.59 + 3.2)**

**On further calculation**

**= 36 â€“ 21.79**

**= 14.21**

**(iv) 86 + 16.95 â€“ 3.0042It can be written as**

**= 102.95 â€“ 3.0042**

**On further calculation**

**= 99.9458**

**(v) 32.8 â€“ 13 â€“ 10.725 +3.517It can be written as**

**= (32.8 + 3.517) â€“ (13 + 10.725)**

**On further calculation**

**= 36.317 â€“ 23.725**

**= 12.592**

**(vi) 4000 â€“ 30.51 â€“ 753.101 â€“ 69.43It can be written as**

**= 4000 â€“ (30.51 + 753.101 + 69.43)**

**On further calculation**

**= 4000 â€“ 853.041**

**= 3146.959**

**(vii) 0.1835 + 163.2005 â€“ 25.9 â€“ 100It can be written as**

**= (0.1835 + 163.2005) â€“ (25.9 + 100)**

**On further calculation**

**= 163.2840 â€“ 125.9 **

**= 37.484**

**(viii) 38.00 â€“ 30 + 200.200 â€“ 0.230It can be written as**

**= (38.00 + 200.200) â€“ (30 + 0.230)**

**On further calculation**

**= 238.200 â€“ 30.230**

**= 207.970**

**= 207.97**

**(ix) 555.555 + 55.555 â€“ 5.55 â€“ 0.555**

**It can be written as**

**= (555.555 + 55.555) â€“ (5.55 + 0.555)**

**On further calculation**

**= 611.110 â€“ 6.105**

**= 605.005**

**4. Find the difference between 6.85 and 0.685.**

**Solution:**

The difference between 6.85 and 0.685 = 6.85 â€“ 0.685

= 6.165

**5. Take out the sum of 19.38 and 56.025, then subtract it from 200.111.**

**Solution:**

We know that the sum of 19.38 and 56.025 can be written as

19.38 + 56.025 = 75.405

We can write it as

Difference between 200.111 and 75.405

200.111 â€“ 75.405 = 124.706

**6. Add 13.95 and 1.003, and from the result, subtract the sum of 2.794 and 6.2.**

**Solution:**

We know that addition of 13.95 and 1.003 can be written as

13.95 + 1.003 = 14.953

Similarly the sum of 2.794 and 6.2 can be written as

2.794 + 6.2 = 8.994

Here the difference between 14.953 and 8.994

14.953 â€“ 8.994 = 5.959

**7. What should be added to 39.587 to give 80.375?**

**Solution:**

It is given that

Sum of two numbers = 80.375

One number = 39.587

So the other number = 80.375 â€“ 39.587 = 40.788

**8. What should be subtracted from 100 to give 19.29?**

**Solution:**

**It is given that**

**Sum of two numbers = 100**

**One number = 19.29**

**So the other number = 100 â€“ 19.29 = 80.71**

**9. What is the excess of 584.29 over 213.95?**

**Solution:**

**It is given that**

**Sum of two numbers = 584.29**

**One number = 213.95**

**So the other number = 584.29 â€“ 213.95 = 370.34**

**10. Evaluate: **

**(i) (5.4 â€“ 0.8) + (2.97 -1.462) **

**(ii) (6.25 + 0.36) – (17.2 â€“ 8.97) **

**(iii) 9.004 + (3 -2.462) **

**(iv) 879.4 â€“ (87.94 â€“ 8 .794)**

**Solution:**

**(i) (5.4 â€“ 0.8) + (2.97 -1.462) It can be written as**

**= 4.6 + 1.508**

**On further calculation**

**= 6.108**

**(ii) (6.25 + 0.36) – (17.2 â€“ 8.97) It can be written as**

**= 6.61 â€“ 8.23**

**On further calculation**

**= – 1.62**

**(iii) 9.004 + (3 – 2.462) It can be written as**

**= 9.004 + 0.538**

**On further calculation**

**= 9.542**

**(iv) 879.4 â€“ (87.94 â€“ 8 .794)**

**It can be written as**

**= 879.4 â€“ 79.146**

**On further calculation**

**= 800.254**

**11. What is the excess of 75 over 48.29?**

**Solution:**

**We know that the excess of 75 over 48.29 can be written as**

**Hence, the excess of 75 over 48.29 is 26.71.**

**12. If A = 237.98 and B = 83.47.**

**Find: **

**(i) A â€“ B **

**(ii) B â€“ A.**

**Solution:**

**(i) A â€“ B **

**It is given that A = 237.98 and B = 83.47**

**Substituting the values**

**A â€“ B = 237.98 â€“ 83.47 **

**A â€“ B = 154.51**

**(ii) B â€“ A**

**It is given that A = 237.98 and B = 83.47**

**Substituting the values**

**B â€“ A = 83.47 â€“ 237.98 **

**B â€“ A = – 154.51**

**13. The cost of one kg of sugar increases from **â‚¹**28.47 to **â‚¹**32.65. Find the increase in cost.**

**Solution:**

**Cost of sugar = **â‚¹**28.47**

**Cost of sugar is raised = **â‚¹**32.65**

**Increase in the cost of sugar = **â‚¹**32.65 – **â‚¹**28.47 = **â‚¹**4.18**

#### Exercise 4C page: 61

**1. Multiply:**

**(i) 0.87 by 10**

**(ii) 2.948 by 100**

**(iii) 6.4 by 1000**

**(iv) 5.8 by 4**

**(v) 16.32 by 28**

**(vi) 5. 037 by 8**

**(vi) 4.6 by 2.1**

**(viii) 0.568 by 6.4**

**Solution:**

**(i) 0.87 by 10It can be written as**

**0.87 Ã— 10 = 8.7**

**(ii) 2.948 by 100It can be written as**

**2.948 Ã— 100 = 294.8**

**(iii) 6.4 by 1000It can be written as**

**6.4 Ã— 1000 = 6400**

**(iv) 5.8 by 4It can be written as**

**5.8 Ã— 4 = 23.2 **

**(v) 16.32 by 28It can be written as**

**16.32 Ã— 28 = 456.96**

**(vi) 5.037 by 8It can be written as**

**5.037 Ã— 8 = 40.296**

**(vi) 4.6 by 2.1It can be written as**

**4.6 Ã— 2.1 = 9.66**

**(viii) 0.568 by 6.4**

**It can be written as**

**0.568 Ã— 6.4 = 3.6352**

**2. Multiply each number by 10, 100, 1000: **

**(i) 0.5**

**(ii) 0.112**

**(iii) 4.8**

**(iv) 0.0359**

**(v) 16.27**

**(vi) 234.8**

**Solution:**

**(i) 0.5It can be written as**

**0.5 Ã— 10 = 5**

**0.5 Ã— 100 = 50**

**0.5 Ã— 1000 = 500**

**(ii) 0.112It can be written as**

**0.112 Ã— 10 = 1.12**

**0.112 Ã— 100 = 11.2**

**0.112 Ã— 1000 = 112**

**(iii) 4.8It can be written as**

**4.8 Ã— 10 = 48**

**4.8 Ã— 100 = 480**

**4.8 Ã— 1000 = 4800**

**(iv) 0.0359It can be written as**

**0.0359 Ã— 10 = 0.359**

**0.0359 Ã— 100 = 3.59**

**0.0359 Ã— 1000 = 35.9**

**(v) 16.27It can be written as**

**16.27 Ã— 10 = 162.7**

**16.27 Ã— 100 = 1627**

**16.27 Ã— 1000 = 16270**

**(vi) 234.8**

**It can be written as**

**234.8 Ã— 10 = 2348**

**234.8 Ã— 100 = 23480**

**234.8 Ã— 1000 = 234800**

**3. Evaluate:**

**(i) 5.897 x 2.3**

**(ii) 0.894 x 87**

**(iii) 0.01 x 0.001**

**(iv) 0.84 x 2.2 x 4**

**(v) 4.75 x 0.08 x 3**

**(vi) 2.4 x 3.5 x 4.8**

**(vii) 0.8 x 1.2 x 0.25**

**(viii) 0.3 x 0.03 x 0.003**

**Solution:**

**(i) 5.897 x 2.3We know that **

**5.897 x 2.3 = 13.5631**

**(ii) 0.894 x 87We know that**

**0.894 x 87 = 77.778**

**(iii) 0.01 x 0.001We know that**

**0.01 x 0.001 = **0.00001

**(iv) 0.84 x 2.2 x 4It can be written as**

**= 0.84 x 8.8**

**= 7.392**

**(v) 4.75 x 0.08 x 3It can be written as**

**= 4.75 x 0.24**

**= 1.1400**

**= 1.14**

**(vi) 2.4 x 3.5 x 4.8It can be written as**

**= 8.40 x 4.8**

**= 8.4 x 4.8**

**We get**

**= 40.32**

**(vii) 0.8 x 1.2 x 0.25It can be written as**

**= 0.96 x 0.25= 0.2400**

**= 0.24**

**(viii) 0.3 x 0.03 x 0.003**

**It can be written as**

**= 0.009 x 0.003**

**= 0.000027**

**4. Divide: **

**(i) 54.9 by 10**

**(ii) 7.8 by 100**

**(iii) 324.76 by 1000**

**(iv) 12.8 by 4**

**(v) 27.918 by 9**

**(vi) 4.672 by 8**

**(vii) 4.32 by 1.2**

**(viii) 7.644 by 1.4**

**(ix) 4.8432 by 0.08**

**Solution:**

**(i) 54.9 by 10It can be written as**

**54.9 **Ã· 10 = 5.49

**(ii) 7.8 by 100It can be written as**

**7.8 **Ã· 100 = 0.078

**(iii) 324.76 by 1000It can be written as**

**324.76 **Ã· 1000 = 0.32476

**(iv) 12.8 by 4It can be written as**

**12.8 **Ã· 4 = 3.2

**(v) 27.918 by 9It can be written as**

**27.918 **Ã· 9 = 3.102

**(vi) 4.672 by 8**

**It can be written as**

**4.672 **Ã· 8 = 0.584

**(vii) 4.32 by 1.2It can be written as**

**4.32 **Ã· 1.2

Multiplying by 100

432 Ã· 120 = 3.6

**(viii) 7.644 by 1.4It can be written as**

**7.644 **Ã· 1.4

Multiplying by 1000

7644 Ã· 1400 = 5.46

**(ix) 4.8432 by 0.08**

**It can be written as**

**4.8432 **Ã· 0.08

**So we get**

**48432 **Ã· 800 = 60.54

**5. Divide each of the given numbers by 10, 100, 1000 and 10000**

**(i) 2.1**

**(ii) 8.64**

**(iii) 5-01**

**(iv) 0.0906**

**(v) 0.125**

**(vi) 111.11**

**Solution:**

**(i) 2.1It can be written as**

**2.1 **Ã· 10 = 0.21

2.1 Ã· 100 = 0.021

2.1 Ã· 1000 = 0.0021

2.1 Ã· 10000 = 0.00021

**(ii) 8.64It can be written as**

**8.64 **Ã· 10 = 0.864

8.64 Ã· 100 = 0.0864

8.64 Ã· 1000 = 0.00864

8.64 Ã· 10000 = 0.000864

**(iii) 5.01It can be written as**

**5.01 **Ã· 10 = 0.501

5.01 Ã· 100 = 0.0501

5.01 Ã· 1000 = 0.00501

5.01 Ã· 10000 = 0.000501

**(iv) 0.0906It can be written as**

**0.0906 **Ã· 10 = 0.00906

0.0906 Ã· 100 = 0.000906

0.0906 Ã· 1000 = 0.0000906

0.0906 Ã· 10000 = 0.00000906

**(v) 0.125It can be written as**

**0.125 **Ã· 10 = 0.0125

0.125 Ã· 100 = 0.00125

0.125 Ã· 1000 = 0.000125

0.125 Ã· 10000 = 0.0000125

**(vi) 111.11**

**It can be written as**

**111.11 **Ã· 10 = 11.111

**111.11 **Ã· 100 = 1.1111

111.11 Ã· 1000 = 0.11111

111.11 Ã· 10000 = 0.011111

**6. Evaluate :**

**(i) 9.75 **Ã·** 5**

**(ii) 4.4064 **Ã·** 4 **

**(iii) 27.69 **Ã·** 30**

**(iv) 19.25 **Ã·** 25**

**(v) 20.64 **Ã·** 16**

**(vi) 3.204 **Ã·** 9**

**(vii) 0.125 **Ã·** 25**

**(viii) 0.14616 **Ã·** 72**

**(ix) 0.6227 **Ã·** 1300**

**(x) 257.894 **Ã·** 0.169**

**(xi) 6.3 **Ã·** (0.3)Â²**

**Solution:**

**(i) 9.75 Ã· 5We get**

**9.75 Ã· 5 = 1.95**

**(ii) 4.4064 Ã· 4 We get**

**4.4064 Ã· 4 = 1.016**

**(iii) 27.69 Ã· 30We get**

**27.69 Ã· 30 = 0.923**

**(iv) 19.25 Ã· 25We get**

**19.25 Ã· 25 = 0.77**

**(v) 20.64 Ã· 16We get**

**20.64 Ã· 16 = 1.29**

**(vi) 3.204 Ã· 9We get**

**3.204 Ã· 9 = 0.356**

**(vii) 0.125 Ã· 25We get**

**0.125 Ã· 25 = 0.005**

**(viii) 0.14616 Ã· 72We get**

**0.14616 Ã· 72 = 0.00203**

**(ix) 0.6227 Ã· 1300We get**

**0.6227 Ã· 1300 = 0.000479**

**(x) 257.894 Ã· 0.169Multiplying by 1000**

**257894 Ã· **169 = 1526

**(xi) 6.3 Ã· (0.3)Â²**

**We can write it as**

**= 6.3 **Ã·** **(0.3 Ã— 0.3)

**By further calculation**

**= 6.3 **Ã· 0.09

Multiply both sides by 100

= 630 Ã· 9 = 70

**7. Evaluate: **

**(i) 4.3 x 0.52 x 0.3**

**(ii) 3.2 x 2.5 x 0.7**

**(iii) 0.8 x 1.5 x 0.6**

**(iv) 0.3 x 0.3 x 0.3**

**(v) 1.2 x 1.2 x 0.4**

**(vi) 0.4 x 0.04 x 0.004**

**(vii) 0.5 x 0.6 x 0.7**

**(viii) 0.5 x 0.06 x 0.007**

**Solution:**

**(i) 4.3 x 0.52 x 0.3We know that**

**Here the sum of decimal places = 1 + 2 + 1 = 4**

**So we get**

**4.3 x 0.52 x 0.3 = 0.6708**

**(ii) 3.2 x 2.5 x 0.7We know that**

**Here the sum of decimal places = 1 + 1 + 1 = 3**

**So we get**

**3.2 x 2.5 x 0.7 = 5.600 or 5.6**

**(iii) 0.8 x 1.5 x 0.6We know that**

**Here the sum of decimal places = 1 + 1 + 1 = 3**

**So we get**

**0.8 x 1.5 x 0.6 **= 0.720 or 0.72

**(iv) 0.3 x 0.3 x 0.3We know that**

**Here the sum of decimal places = 1 + 1 + 1 = 3**

**So we get**

**0.3 x 0.3 x 0.3 = **0.027

**(v) 1.2 x 1.2 x 0.4We know that **

** **

**Here the sum of decimal places = 1 + 1 + 1 = 3**

**So we get**

**1.2 x 1.2 x 0.4 = 0.576**

**(vi) 0.4 x 0.04 x 0.004We know that**

**Here the sum of decimal places = 1 + 2 + 3 = 6**

**So we get**

**0.4 x 0.04 x 0.004 = 0.000064**

**(vii) 0.5 x 0.6 x 0.7**

**We know that**

**Here the sum of decimal places = 1 + 1 + 1 = 3**

**So we get**

**0.5 x 0.6 x 0.7 = 0.210 or 0.21**

**(viii) 0.5 x 0.06 x 0.007**

**We know that**

**Here the sum of decimal places = 1 + 2 + 3 = 5**

**So we get**

**0.5 x 0.06 x 0.007 = 0.00021**

**8. Evaluate: **

**(i) (0.9)Â²**

**(ii) (0.6)Â² x 0.5**

**(iii) 0.3 x (0.5)Â²**

**(iv) (0.4)Â³**

**(v) (0.2) ^{3}Â x 5**

**(vi) (0.2)**

^{3}Â x 0.05**Solution:**

**(i) (0.9)Â²It can be written as**

**0.9 x 0.9 = 0.81**

**Here the sum of decimal places is 1 + 1 = 2**

**(ii) (0.6)Â² x 0.5It can be written as**

**= 0.6 x 0.6 x 0.5**

**On further calculation**

**= 0.36 x 0.5 **

**= 0.180 or 0.18**

**Here the sum of decimal places is 1 + 1 + 1 = 3**

**(iii) 0.3 x (0.5)Â²It can be written as**

**= 0.3 x 0.5 x 0.5**

**On further calculation**

**= 0.3 x 0.25 **

**= 0.075**

**Here the sum of decimal places is 1 + 1 + 1 = 3**

**(iv) (0.4)Â³It can be written as**

**= 0.4 x 0.4 x 0.4**

**On further calculation**

**= 0.16 x 0.4 **

**= 0.064**

**Here the sum of decimal places is 1 + 1 + 1 = 3**

**(v) (0.2) ^{3}Â x 5It can be written as**

**= 0.2 x 0.2 x 0.2 x 5**

**On further calculation**

**= 0.008 x 5**

**= 0.40 or 0.4**

**Here the sum of decimal places is 1 + 1 + 1 = 3**

**(vi) (0.2) ^{3}Â x 0.05**

**It can be written as**

**= 0.2 x 0.2 x 0.2 x** 0.05

**On further calculation**

**= 0.008 x 0.05**

**= 0.00040 **

**Here the sum of decimal places is 1 + 1 + 1 + 1 + 1 = 5**

**9. Find the cost of 36.75 kg wheat at the rate of â‚¹12.80 per kg.**

**Solution:**

**It is given that**

**Weight of wheat = 36.75 kg**

**Cost of wheat per kg = â‚¹12.80**

**So the cost of 36.75 kg wheat = 36.75 x 12.80 = â‚¹470.40**

**10. The cost of a pen is â‚¹56.15. Find the cost of 16 such pens.**

**Solution:**

**It is given that**

**Cost of a pen = â‚¹56.15**

**So the cost of 16 such pens = 16 x 56.15 = â‚¹898.40**

**11. Evaluate: **

**(i) 0.0072 Ã· 0.06**

**(ii) 0.621 Ã· 0.3**

**(iii) 0.0532 Ã· 0.005**

**(iv) 0.01162 Ã· 0.14**

**(v) (7.5 x 40.4) Ã· 25**

**(vi) 2.1 Ã· (0.1 x 0.1)**

**Solution:**

**(i) 0.0072 Ã· 0.06Multiplying both numerator and denominator by 100**

**= (0.0072 x 100)/ (0.06 x 100)**

**On further calculation**

**= 0.72/6**

**= 0.12**

**(ii) 0.621 Ã· 0.3Multiplying both numerator and denominator by 10**

**= (0.621 x 10)/ (0.3 x 10)**

**On further calculation**

**= 6.21/3**

**= 2.07**

**(iii) 0.0532 Ã· 0.005Multiplying both numerator and denominator by 1000**

**= (0.0532 x 1000)/ (0.005 x 1000)**

**On further calculation**

**= 53.2/5**

**= 10.64**

**(iv) 0.01162 Ã· 0.14Multiplying both numerator and denominator by 100**

**= (0.01162 x 100)/ (0.14 x 100)**

**On further calculation**

**= 1.162/14**

**= 0.083**

**(v) (7.5 x 40.4) Ã· 25It can be written as**

**= 303/25**

**= 12.12**

**(vi) 2.1 Ã· (0.1 x 0.1)**

**Multiplying both numerator and denominator by 100**

**= (2.1 x 100)/ (0.01 x 100)**

**On further calculation**

**= 210/1**

**= 210**

**12. Fifteen identical articles weigh 31.50 kg. Find the weight of each article.**

**Solution:**

**It is given that**

**Total weight of 15 identical articles = 31.50 kg**

**So the weight of each article = 31.50 â€“ 15 = 2.1 kg**

**Hence, the weight of each article is 2.1 kg.**

**13. The product of two numbers is 211.2. If one of these two numbers is 16.5, find the other number.**

**Solution:**

**It is given that**

**Product of two numbers = 211.2**

**One of the two numbers = 16.5**

**So the other number = 211.2 Ã· 16.5**

**On further calculation**

**= (211.2 x 10)/ (16.5 x 10)**

**So we get**

**= 2112/165**

**= 12.8**

**14. One dozen identical articles cost â‚¹45.96. Find the cost of each article.**

**Solution:**

**It is given that**

**Cost of one dozen articles = â‚¹45.96**

**We know that one dozen = 12**

**So the cost of one article = 45.96 Ã· 12 = â‚¹3.83**

#### Exercise 4D page: 65

**1. Find whether the given division forms a terminating decimal or a non-terminating decimal: **

**(i) 3 Ã· 8**

**(ii) 8 Ã· 3**

**(iii) 6Ã· 5**

**(iv) 5 Ã· 6**

**(v) 12.5 Ã· 4**

**(vi) 23 Ã· 0.7**

**(vii) 42 Ã· 9**

**(viii) 0.56Ã· 0.11**

**Solution:**

**(i) 3 Ã· 8We know that**

**3 Ã· 8 = 0.375**

**Therefore, it is terminating decimal.**

**(ii) 8 Ã· 3We know that**

**8 Ã· 3 = 2.666**

**Therefore, it is a non-terminating decimal.**

**(iii) 6 Ã· 5We know that**

**6 Ã· 5 = 1.2**

**Therefore, it is terminating decimal.**

**(iv) 5 Ã· 6We know that**

**5 Ã· 6 = 0.8333**

**Therefore, it is non-terminating decimal.**

**(v) 12.5 Ã· 4We know that**

**12.5 Ã· 4 = 3.125**

**Therefore, it is terminating decimal. **

**(vi) 23 Ã· 0.7Multiplying by 10 we get**

**230 Ã· 7 = 32.8571428**

**Therefore, it is non-terminating decimal.**

**(vii) 42 Ã· 9We know that**

**42 Ã· 9 = 4.666 **

**Therefore, it is non-terminating decimal.**

**(viii) 0.56 Ã· 0.11**

**Multiplying by 100**

**56 Ã· 11 = 5.0909**

**Therefore, it is non-terminating decimal.**

**2. Express as recurring decimals:**

**(i) 1 1/3**

**(ii) 10/11**

**(iii) 5/6**

**(iv) 2/13**

**(v) 1/9**

**(vi) 17/90**

**(vii) 5/18**

**(viii) 7/12**

**Solution:**

**(i) 1 1/3**

**It can be written as**

**1 1/3 = 4/3 **

**(ii) 10/11**

**It can be written as**

**10/11 = 0.909090â€¦ **

**(iii) 5/6**

**It can be written as**

**5/6 = 0.8333â€¦. **

**(iv) 2/13**

**It can be written as**

**2/13 = 0.153846153846 **

**(v) 1/9**

**It can be written as**

**1/9 = 0.1111 â€¦. **

**(vi) 17/90**

**It can be written as**

**17/90 = 0.1888 **

**(vii) 5/18**

**It can be written as**

**5/18 = 0.2777 â€¦ **

**(viii) 7/12**

**It can be written as**

**7/12 = 0.58333â€¦. **

**3. Convert into vulgar fraction:**

**Solution:**

**It can be written as**

**= 3/9**

**So we get**

**= (3 â€“ 0)/ 9**

**= 3/9**

**= 1/3**

**It can be written as**

**= 8/9**

**So we get**

**= (8 â€“ 0)/ 9 **

**= 8/9**

**It can be written as**

**= 44/9**

**So we get**

**= (44 â€“ 4)/ 9**

**= 40/9**

**= 4 4/9**

**It can be written as**

**= 237/9**

**So we get**

**= (237 â€“ 23)/ 9**

**= 214/9**

**= 23 7/9**

**4. Convert into vulgar fraction:**

**Solution:**

**It can be written as**

**= 35/99**

**So we get**

**= (35 â€“ 0)/ 99 **

**= 35/99**

**It can be written as**

**So we get**

**= 2 + (23 â€“ 0)/ 99**

**On further calculation**

**= 2 + 23/99**

**= 2 33/99**

**It can be written as**

**So we get**

**= 1 + (28 â€“ 0)/ 99**

**On further calculation**

**= 1 + 28/99**

**= 1 28/99**

**It can be written as**

**So we get**

**= 5 + (234 â€“ 0)/ 999**

**On further calculation**

**= 5 234/999**

**5. Convert into vulgar fraction:**

**Solution:**

**It can be written as**

**= (37 â€“ 3)/ 90**

**So we get**

**= 34/90**

**= 17/45**

**It can be written as**

**= (245 â€“ 2)/ 990**

**So we get**

**= 243/990**

**On further calculation**

**= 81/330**

**= 27/110**

**It can be written as**

**= (685 â€“ 68)/ 900**

**So we get**

**= 617/ 900**

**It can be written as**

**= (442 â€“ 4)/ 990**

**So we get**

**= 438/ 990**

**= 219/ 495**

#### Exercise 4E PAGE: 67

**1. Round off:**

**(i) 0.07, 0.112, 3.59, 9.489 to the nearest tenths.**

**(ii) 0.627, 100.479, 0.065 and 0.024 to the nearest hundredths.**

**(iii) 4.83, 0.86, 451.943 and 9.08 to the nearest whole number.**

**Solution:**

**(i) We know that**

**0.07 = 0.1**

**0.112 = 0.1**

**3.59 = 3.6**

**9.489 = 9.5**

**(ii) 0.627 = 0.63**

**100.479 = 100.48**

**0.065 = 0.07**

**0.024 = 0.02**

**(iii) 4.83 = 5**

**0.86 = 1**

**451.943 = 452**

**9.08 = 9**

**2. Simplify, and write your answers correct to the nearest hundredths:**

**(i) 18.35 Ã— 1.2**

**(ii) 62.89 Ã— 0.02**

**Solution:**

**(i) 18.35 Ã— 1.2 = 22.02**

**(ii) 62.89 Ã— 0.02 = 1.2578 = 1.26**

**3. Write the number of significant figures (digits) in:**

**(i) 35.06**

**(ii) 0.35**

**(iii) 7.0068**

**(iv) 19.0**

**(v) 0.0062**

**(vi) 4.2 Ã— 0.6**

**(vii) 0.08 Ã— 25**

**(viii) 3.6 Ã· 0.12**

**Solution:**

**(i) The number of significant figures in 35.06 is 4.**

**(ii) The number of significant figures in 0.35 is 2.**

**(iii) The number of significant figures in 7.0068 is 5.**

**(iv) The number of significant figures in 19.0 is 3.**

**(v) The number of significant figures in 0.0062 is 2.**

**(vi) The number of significant figures in 4.2 Ã— 0.6 = 2.52 is 3.**

**(vii) The number of significant figures in 0.08 Ã— 25 = 2.00 = 2 is 1.**

**(viii) The number of significant figures in 3.6 Ã· 0.12 or 360 Ã· 12 = 30 is 2.**

**4. Write:**

**(i) 35.869, 0.008426, 4.952 and 382.7 correct to three significant figures.**

**(ii) 60.974, 2.8753, 0.001789 and 400.04 correct to four significant figures.**

**(iii) 14.29462, 19.2, 46356.82 and 69 correct to five significant figures.**

**Solution:**

**(i) Here by correcting to three significant figures.**

**35.869 = 35.9**

**0.008426 = 0.00843**

**4.952 = 4.95**

**382.7 = 383**

**(ii) Here by correcting to four significant figures**

**60.974 = 60.97**

**2.8753 = 2.875**

**0.001789 = 0.001789**

**400.04 = 400.0**

**(iii) Here by correcting to five significant figures**

**14.29462 = 14.295**

**19.2 = 19.200**

**46356.82 = 46357**

**69 = 69.000**

#### Exercise 4F page: 67

**1. The weight of an object is 3.06 kg. Find the total weight of 48 similar objects.**

**Solution:**

**It is given that**

**Weight of an object = 3.06 kg**

**So the weight of 48 objects = 3.06 Ã— 48 = 146.88 kg**

**2. Find the cost of 17.5 m cloth at the rate of â‚¹ 112.50 per metre.**

**Solution:**

It is given that

Cost of cloth per metre = â‚¹ 112.50

So the cost of 17.5 m cloth = â‚¹ 112.50 Ã— 17.5

On further calculation

= â‚¹ 1968.750

= â‚¹ 1968.75

**3. One kilogramme of oil costs â‚¹ 73.40. Find the cost of 9.75 kilogramme of the oil.**

**Solution:**

It is given that

Cost of 1 kg oil = â‚¹ 73.40

So the cost of 9.75 kg oil = â‚¹ 73.40 Ã— 9.75

On further calculation

= â‚¹ 715.6500

= â‚¹ 715.65

**4. Total weight of 8 identical objects is 51.2 kg. Find the weight of each object.**

**Solution:**

It is given that

Weight of 8 identical objects = 51.2 kg

So the weight of 1 object = 51.2 Ã· 8 = 6.4 kg

**5. 18.5 m of cloth costs â‚¹ 666. Find the cost of 3.8 m cloth.**

**Solution:**

It is given that

Cost of 18.5 m cloth = â‚¹ 666

So the cost of 1m cloth = â‚¹ 666 Ã· 18.5 and cost of 3.8 m cloth

We can write it as

= (666 Ã· 18.5) Ã— 3.8

Multiplying by 10

= (6660 Ã· 185) Ã— 3.8

= 36 Ã— 3.8

So we get

= â‚¹ 136.80

**6. Find the value of:**

**(i) 0.5 of â‚¹ 7.60 + 1.62 of â‚¹ 30**

**(ii) 2.3 of 7.3 kg + 0.9 of 0.48 kg**

**(iii) 6.25 of 8.4 â€“ 4.7 of 3.24**

**(iv) 0.98 of 235 â€“ 0.09 of 3.2**

**Solution:**

(i) 0.5 of â‚¹ 7.60 + 1.62 of â‚¹ 30

It can be written as

= â‚¹ 3.80 + â‚¹ 48.60

So we get

= â‚¹ 52.40

(ii) 2.3 of 7.3 kg + 0.9 of 0.48 kg

It can be written as

= 16.79 kg + 0.432 kg

So we get

= 17.222 kg

(iii) 6.25 of 8.4 â€“ 4.7 of 3.24

It can be written as

= 52.500 â€“ 15.228

So we get

= 37.272

(iv) 0.98 of 235 â€“ 0.09 of 3.2

It can be written as

= 230.30 â€“ 0.288

So we get

= 230.012

**7. Evaluate:**

**(i) 5.6 â€“ 1.5 of 3.4**

**(ii) 4.8 Ã· 0.04 of 5**

**(iii) 0.72 of 80 Ã· 0.2**

**(iv) 0.72 Ã· 80 of 0.2**

**(v) 6.45 Ã· (3.9 â€“ 1.75)**

**(vi) 0.12 of (0.104 â€“ 0.02) + 0.36 Ã— 0.5**

**Solution:**

(i) 5.6 â€“ 1.5 of 3.4

It can be written as

= 5.6 â€“ 5.1

So we get

= 0.5

(ii) 4.8 Ã· 0.04 of 5

It can be written as

= 4.8 Ã· 0.20

Multiplying by 10

= 48 Ã· 2

= 24

(iii) 0.72 of 80 Ã· 0.2

It can be written as

= 57.60 Ã· 0.2

Multiplying by 10

= 576 Ã· 2

= 288

(iv) 0.72 Ã· 80 of 0.2

It can be written as

= 0.72 Ã· 16.0

Multiplying by 100

= 72 Ã· 1600

= 0.045

(v) 6.45 Ã· (3.9 â€“ 1.75)

It can be written as

= 6.45 Ã· 2.15

Multiplying by 100

= 645 Ã· 215

= 3

(vi) 0.12 of (0.104 â€“ 0.02) + 0.36 Ã— 0.5

**It can be written as**

**= 0.12 of 0.084 + 0.36 Ã— 0.5**

**So we get**

**= 0.01008 + 0.180**

**= 0.19008**