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 BYJU’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 ÷ 25)/ (100 ÷ 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 ÷ 4)/ (100 ÷ 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 ÷ 5)/ (100 ÷ 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 ÷ 5)/ (1000 ÷ 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 ÷ 5)/ (1000 ÷ 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 ÷ 25)/ (1000 ÷ 25)
So we get
= 321/ 40
2. Convert into decimal fractions:
(i) 2 4/5
(ii) 79/100
(iii) 37/10,000
(iv) 7543/104
(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 × 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) 7543/104
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, 9.8
It can be written as
9.8 – 5.4 = 4.4
(ii) 0.16, 4.3
It can be written as
4.3 – 0.16 = 4.14
(iii) 0.82, 8.6
It can be written as
8.6 – 0.82 = 7.78
(v) 2.237, 9.425
It can be written as
9.425 – 2.237 = 7.188
(vi) 41 .03, 59.46
It can be written as
59.46 – 41.03 = 18.43
(vii) 3.92, 26.86
It can be written as
26.86 – 3.92 = 22.94
(viii) 4.73, 8.5
It can be written as
8.5 – 4.73 = 3.77
(ix) 12.63, 36.2
It can be written as
36.2 – 12.63 = 23.57
(x) 0.845, 3.71
It can be written as
3.71 – 0.845 = 2.865
3. Simplify:
(i) 28.796 -13.42 – 2.555
(ii) 93.354 – 62.82 – 13.045
(iii) 36 – 18.59 – 3.2
(iv) 86 + 16.95 – 3.0042
(v) 32.8 – 13 – 10.725 +3.517
(vi) 4000 – 30.51 – 753.101 – 69.43
(vii) 0.1835 + 163.2005 – 25.9 – 100
(viii) 38.00 – 30 + 200.200 – 0.230
(ix) 555.555 + 55.555 – 5.55 – 0.555
Solution:
(i) 28.796 -13.42 – 2.555
It can be written as
= 28.796 – (13.42 + 2.555)
On further calculation
= 28.796 – 15.975
= 12.821
(ii) 93.354 – 62.82 – 13.045
It can be written as
= 93.354 – (62.82 + 13.045)
On further calculation
= 93.354 – 75.865
= 17.489
(iii) 36 – 18.59 – 3.2
It can be written as
= 36 – (18.59 + 3.2)
On further calculation
= 36 – 21.79
= 14.21
(iv) 86 + 16.95 – 3.0042
It can be written as
= 102.95 – 3.0042
On further calculation
= 99.9458
(v) 32.8 – 13 – 10.725 +3.517
It can be written as
= (32.8 + 3.517) – (13 + 10.725)
On further calculation
= 36.317 – 23.725
= 12.592
(vi) 4000 – 30.51 – 753.101 – 69.43
It can be written as
= 4000 – (30.51 + 753.101 + 69.43)
On further calculation
= 4000 – 853.041
= 3146.959
(vii) 0.1835 + 163.2005 – 25.9 – 100
It can be written as
= (0.1835 + 163.2005) – (25.9 + 100)
On further calculation
= 163.2840 – 125.9
= 37.484
(viii) 38.00 – 30 + 200.200 – 0.230
It can be written as
= (38.00 + 200.200) – (30 + 0.230)
On further calculation
= 238.200 – 30.230
= 207.970
= 207.97
(ix) 555.555 + 55.555 – 5.55 – 0.555
It can be written as
= (555.555 + 55.555) – (5.55 + 0.555)
On further calculation
= 611.110 – 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 – 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 – 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 – 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 – 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 – 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 – 213.95 = 370.34
10. Evaluate:
(i) (5.4 – 0.8) + (2.97 -1.462)
(ii) (6.25 + 0.36) – (17.2 – 8.97)
(iii) 9.004 + (3 -2.462)
(iv) 879.4 – (87.94 – 8 .794)
Solution:
(i) (5.4 – 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 – 8.97)
It can be written as
= 6.61 – 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 – (87.94 – 8 .794)
It can be written as
= 879.4 – 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 – B
(ii) B – A.
Solution:
(i) A – B
It is given that A = 237.98 and B = 83.47
Substituting the values
A – B = 237.98 – 83.47
A – B = 154.51
(ii) B – A
It is given that A = 237.98 and B = 83.47
Substituting the values
B – A = 83.47 – 237.98
B – A = – 154.51
13. The cost of one kg of sugar increases from ₹28.47 to ₹32.65. Find the increase in cost.
Solution:
Cost of sugar = ₹28.47
Cost of sugar is raised = ₹32.65
Increase in the cost of sugar = ₹32.65 – ₹28.47 = ₹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 10
It can be written as
0.87 × 10 = 8.7
(ii) 2.948 by 100
It can be written as
2.948 × 100 = 294.8
(iii) 6.4 by 1000
It can be written as
6.4 × 1000 = 6400
(iv) 5.8 by 4
It can be written as
5.8 × 4 = 23.2
(v) 16.32 by 28
It can be written as
16.32 × 28 = 456.96
(vi) 5.037 by 8
It can be written as
5.037 × 8 = 40.296
(vi) 4.6 by 2.1
It can be written as
4.6 × 2.1 = 9.66
(viii) 0.568 by 6.4
It can be written as
0.568 × 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) 0.5
It can be written as
0.5 × 10 = 5
0.5 × 100 = 50
0.5 × 1000 = 500
(ii) 0.112
It can be written as
0.112 × 10 = 1.12
0.112 × 100 = 11.2
0.112 × 1000 = 112
(iii) 4.8
It can be written as
4.8 × 10 = 48
4.8 × 100 = 480
4.8 × 1000 = 4800
(iv) 0.0359
It can be written as
0.0359 × 10 = 0.359
0.0359 × 100 = 3.59
0.0359 × 1000 = 35.9
(v) 16.27
It can be written as
16.27 × 10 = 162.7
16.27 × 100 = 1627
16.27 × 1000 = 16270
(vi) 234.8
It can be written as
234.8 × 10 = 2348
234.8 × 100 = 23480
234.8 × 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 2.3
We know that
5.897 x 2.3 = 13.5631
(ii) 0.894 x 87
We know that
0.894 x 87 = 77.778
(iii) 0.01 x 0.001
We know that
0.01 x 0.001 = 0.00001
(iv) 0.84 x 2.2 x 4
It can be written as
= 0.84 x 8.8
= 7.392
(v) 4.75 x 0.08 x 3
It can be written as
= 4.75 x 0.24
= 1.1400
= 1.14
(vi) 2.4 x 3.5 x 4.8
It 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 0.25
It 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 10
It can be written as
54.9 ÷ 10 = 5.49
(ii) 7.8 by 100
It can be written as
7.8 ÷ 100 = 0.078
(iii) 324.76 by 1000
It can be written as
324.76 ÷ 1000 = 0.32476
(iv) 12.8 by 4
It can be written as
12.8 ÷ 4 = 3.2
(v) 27.918 by 9
It can be written as
27.918 ÷ 9 = 3.102
(vi) 4.672 by 8
It can be written as
4.672 ÷ 8 = 0.584
(vii) 4.32 by 1.2
It can be written as
4.32 ÷ 1.2
Multiplying by 100
432 ÷ 120 = 3.6
(viii) 7.644 by 1.4
It can be written as
7.644 ÷ 1.4
Multiplying by 1000
7644 ÷ 1400 = 5.46
(ix) 4.8432 by 0.08
It can be written as
4.8432 ÷ 0.08
So we get
48432 ÷ 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) 2.1
It can be written as
2.1 ÷ 10 = 0.21
2.1 ÷ 100 = 0.021
2.1 ÷ 1000 = 0.0021
2.1 ÷ 10000 = 0.00021
(ii) 8.64
It can be written as
8.64 ÷ 10 = 0.864
8.64 ÷ 100 = 0.0864
8.64 ÷ 1000 = 0.00864
8.64 ÷ 10000 = 0.000864
(iii) 5.01
It can be written as
5.01 ÷ 10 = 0.501
5.01 ÷ 100 = 0.0501
5.01 ÷ 1000 = 0.00501
5.01 ÷ 10000 = 0.000501
(iv) 0.0906
It can be written as
0.0906 ÷ 10 = 0.00906
0.0906 ÷ 100 = 0.000906
0.0906 ÷ 1000 = 0.0000906
0.0906 ÷ 10000 = 0.00000906
(v) 0.125
It can be written as
0.125 ÷ 10 = 0.0125
0.125 ÷ 100 = 0.00125
0.125 ÷ 1000 = 0.000125
0.125 ÷ 10000 = 0.0000125
(vi) 111.11
It can be written as
111.11 ÷ 10 = 11.111
111.11 ÷ 100 = 1.1111
111.11 ÷ 1000 = 0.11111
111.11 ÷ 10000 = 0.011111
6. Evaluate :
(i) 9.75 ÷ 5
(ii) 4.4064 ÷ 4
(iii) 27.69 ÷ 30
(iv) 19.25 ÷ 25
(v) 20.64 ÷ 16
(vi) 3.204 ÷ 9
(vii) 0.125 ÷ 25
(viii) 0.14616 ÷ 72
(ix) 0.6227 ÷ 1300
(x) 257.894 ÷ 0.169
(xi) 6.3 ÷ (0.3)²
Solution:
(i) 9.75 ÷ 5
We get
9.75 ÷ 5 = 1.95
(ii) 4.4064 ÷ 4
We get
4.4064 ÷ 4 = 1.016
(iii) 27.69 ÷ 30
We get
27.69 ÷ 30 = 0.923
(iv) 19.25 ÷ 25
We get
19.25 ÷ 25 = 0.77
(v) 20.64 ÷ 16
We get
20.64 ÷ 16 = 1.29
(vi) 3.204 ÷ 9
We get
3.204 ÷ 9 = 0.356
(vii) 0.125 ÷ 25
We get
0.125 ÷ 25 = 0.005
(viii) 0.14616 ÷ 72
We get
0.14616 ÷ 72 = 0.00203
(ix) 0.6227 ÷ 1300
We get
0.6227 ÷ 1300 = 0.000479
(x) 257.894 ÷ 0.169
Multiplying by 1000
257894 ÷ 169 = 1526
(xi) 6.3 ÷ (0.3)²
We can write it as
= 6.3 ÷ (0.3 × 0.3)
By further calculation
= 6.3 ÷ 0.09
Multiply both sides by 100
= 630 ÷ 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 0.3
We 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 0.7
We 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 0.6
We 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 0.3
We 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 0.4
We 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 0.004
We 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)²
(ii) (0.6)² x 0.5
(iii) 0.3 x (0.5)²
(iv) (0.4)³
(v) (0.2)3Â x 5
(vi) (0.2)3Â x 0.05
Solution:
(i) (0.9)²
It can be written as
0.9 x 0.9 = 0.81
Here the sum of decimal places is 1 + 1 = 2
(ii) (0.6)² x 0.5
It 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)²
It 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)³
It 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)3Â x 5
It 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)3Â 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 ₹12.80 per kg.
Solution:
It is given that
Weight of wheat = 36.75 kg
Cost of wheat per kg = ₹12.80
So the cost of 36.75 kg wheat = 36.75 x 12.80 = ₹470.40
10. The cost of a pen is ₹56.15. Find the cost of 16 such pens.
Solution:
It is given that
Cost of a pen = ₹56.15
So the cost of 16 such pens = 16 x 56.15 = ₹898.40
11. Evaluate:
(i) 0.0072 ÷ 0.06
(ii) 0.621 ÷ 0.3
(iii) 0.0532 ÷ 0.005
(iv) 0.01162 ÷ 0.14
(v) (7.5 x 40.4) ÷ 25
(vi) 2.1 ÷ (0.1 x 0.1)
Solution:
(i) 0.0072 ÷ 0.06
Multiplying 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 ÷ 0.3
Multiplying 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 ÷ 0.005
Multiplying 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 ÷ 0.14
Multiplying 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) ÷ 25
It can be written as
= 303/25
= 12.12
(vi) 2.1 ÷ (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 – 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 ÷ 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 ₹45.96. Find the cost of each article.
Solution:
It is given that
Cost of one dozen articles = ₹45.96
We know that one dozen = 12
So the cost of one article = 45.96 ÷ 12 = ₹3.83
Exercise 4D page: 65
1. Find whether the given division forms a terminating decimal or a non-terminating decimal:
(i) 3 ÷ 8
(ii) 8 ÷ 3
(iii) 6÷ 5
(iv) 5 ÷ 6
(v) 12.5 ÷ 4
(vi) 23 ÷ 0.7
(vii) 42 ÷ 9
(viii) 0.56÷ 0.11
Solution:
(i) 3 ÷ 8
We know that
3 ÷ 8 = 0.375
Therefore, it is terminating decimal.
(ii) 8 ÷ 3
We know that
8 ÷ 3 = 2.666
Therefore, it is a non-terminating decimal.
(iii) 6 ÷ 5
We know that
6 ÷ 5 = 1.2
Therefore, it is terminating decimal.
(iv) 5 ÷ 6
We know that
5 ÷ 6 = 0.8333
Therefore, it is non-terminating decimal.
(v) 12.5 ÷ 4
We know that
12.5 ÷ 4 = 3.125
Therefore, it is terminating decimal.
(vi) 23 ÷ 0.7
Multiplying by 10 we get
230 ÷ 7 = 32.8571428
Therefore, it is non-terminating decimal.
(vii) 42 ÷ 9
We know that
42 ÷ 9 = 4.666
Therefore, it is non-terminating decimal.
(viii) 0.56 ÷ 0.11
Multiplying by 100
56 ÷ 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 = 0.909090… 
(iii) 5/6
It can be written as
5/6 = 0.8333…. 
(iv) 2/13
It can be written as
2/13 = 0.153846153846 
(v) 1/9
It can be written as
1/9 = 0.1111 …. 
(vi) 17/90
It can be written as
17/90 = 0.1888 
(vii) 5/18
It can be written as
5/18 = 0.2777 … 
(viii) 7/12
It can be written as
7/12 = 0.58333…. 
3. Convert into vulgar fraction:
Solution:
It can be written as
= 3/9
So we get
= (3 – 0)/ 9
= 3/9
= 1/3
It can be written as
= 8/9
So we get
= (8 – 0)/ 9
= 8/9
It can be written as
= 44/9
So we get
= (44 – 4)/ 9
= 40/9
= 4 4/9
It can be written as
= 237/9
So we get
= (237 – 23)/ 9
= 214/9
= 23 7/9
4. Convert into vulgar fraction:
Solution:
It can be written as
= 35/99
So we get
= (35 – 0)/ 99
= 35/99
It can be written as
So we get
= 2 + (23 – 0)/ 99
On further calculation
= 2 + 23/99
= 2 33/99
It can be written as
So we get
= 1 + (28 – 0)/ 99
On further calculation
= 1 + 28/99
= 1 28/99
It can be written as
So we get
= 5 + (234 – 0)/ 999
On further calculation
= 5 234/999
5. Convert into vulgar fraction:
Solution:
It can be written as
= (37 – 3)/ 90
So we get
= 34/90
= 17/45
It can be written as
= (245 – 2)/ 990
So we get
= 243/990
On further calculation
= 81/330
= 27/110
It can be written as
= (685 – 68)/ 900
So we get
= 617/ 900
It can be written as
= (442 – 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 × 1.2
(ii) 62.89 × 0.02
Solution:
(i) 18.35 × 1.2 = 22.02
(ii) 62.89 × 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 × 0.6
(vii) 0.08 × 25
(viii) 3.6 ÷ 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 × 0.6 = 2.52 is 3.
(vii) The number of significant figures in 0.08 × 25 = 2.00 = 2 is 1.
(viii) The number of significant figures in 3.6 ÷ 0.12 or 360 ÷ 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 × 48 = 146.88 kg
2. Find the cost of 17.5 m cloth at the rate of ₹ 112.50 per metre.
Solution:
It is given that
Cost of cloth per metre = ₹ 112.50
So the cost of 17.5 m cloth = ₹ 112.50 × 17.5
On further calculation
= ₹ 1968.750
= ₹ 1968.75
3. One kilogramme of oil costs ₹ 73.40. Find the cost of 9.75 kilogramme of the oil.
Solution:
It is given that
Cost of 1 kg oil = ₹ 73.40
So the cost of 9.75 kg oil = ₹ 73.40 × 9.75
On further calculation
= ₹ 715.6500
= ₹ 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 ÷ 8 = 6.4 kg
5. 18.5 m of cloth costs ₹ 666. Find the cost of 3.8 m cloth.
Solution:
It is given that
Cost of 18.5 m cloth = ₹ 666
So the cost of 1m cloth = ₹ 666 ÷ 18.5 and cost of 3.8 m cloth
We can write it as
= (666 ÷ 18.5) × 3.8
Multiplying by 10
= (6660 ÷ 185) × 3.8
= 36 × 3.8
So we get
= ₹ 136.80
6. Find the value of:
(i) 0.5 of ₹ 7.60 + 1.62 of ₹ 30
(ii) 2.3 of 7.3 kg + 0.9 of 0.48 kg
(iii) 6.25 of 8.4 – 4.7 of 3.24
(iv) 0.98 of 235 – 0.09 of 3.2
Solution:
(i) 0.5 of ₹ 7.60 + 1.62 of ₹ 30
It can be written as
= ₹ 3.80 + ₹ 48.60
So we get
= ₹ 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 – 4.7 of 3.24
It can be written as
= 52.500 – 15.228
So we get
= 37.272
(iv) 0.98 of 235 – 0.09 of 3.2
It can be written as
= 230.30 – 0.288
So we get
= 230.012
7. Evaluate:
(i) 5.6 – 1.5 of 3.4
(ii) 4.8 ÷ 0.04 of 5
(iii) 0.72 of 80 ÷ 0.2
(iv) 0.72 ÷ 80 of 0.2
(v) 6.45 ÷ (3.9 – 1.75)
(vi) 0.12 of (0.104 – 0.02) + 0.36 × 0.5
Solution:
(i) 5.6 – 1.5 of 3.4
It can be written as
= 5.6 – 5.1
So we get
= 0.5
(ii) 4.8 ÷ 0.04 of 5
It can be written as
= 4.8 ÷ 0.20
Multiplying by 10
= 48 ÷ 2
= 24
(iii) 0.72 of 80 ÷ 0.2
It can be written as
= 57.60 ÷ 0.2
Multiplying by 10
= 576 ÷ 2
= 288
(iv) 0.72 ÷ 80 of 0.2
It can be written as
= 0.72 ÷ 16.0
Multiplying by 100
= 72 ÷ 1600
= 0.045
(v) 6.45 ÷ (3.9 – 1.75)
It can be written as
= 6.45 ÷ 2.15
Multiplying by 100
= 645 ÷ 215
= 3
(vi) 0.12 of (0.104 – 0.02) + 0.36 × 0.5
It can be written as
= 0.12 of 0.084 + 0.36 × 0.5
So we get
= 0.01008 + 0.180
= 0.19008
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