Decimal Fractions — Exercise 4(B)

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

Answer

While adding decimals, the decimal points are placed in the same vertical line and empty places are filled with zeros to make like decimals.

(i) Solving,

$\begin{array}{r} 0.50 \\ +0.37 \\ \hline 0.87 \end{array}$

Hence, 0.5 + 0.37 = 0.87

(ii) Solving,

$\begin{array}{r} 3.8 \\ +8.7 \\ \hline 12.5 \end{array}$

Hence, 3.8 + 8.7 = 12.5

(iii) Solving,

$\begin{array}{r} 0.020 \\ 0.008 \\ +0.309 \\ \hline 0.337 \end{array}$

Hence, 0.02 + 0.008 + 0.309 = 0.337

(iv) Solving,

$\begin{array}{r} 0.4136 \\ 0.3195 \\ +0.5200 \\ \hline 1.2531 \end{array}$

Hence, 0.4136 + 0.3195 + 0.52 = 1.2531

(v) Solving,

$\begin{array}{r} 9.250 \\ 3.400 \\ +6.666 \\ \hline 19.316 \end{array}$

Hence, 9.25 + 3.4 + 6.666 = 19.316

(vi) Solving,

$\begin{array}{r} 3.007 \\ 0.587 \\ +18.341 \\ \hline 21.935 \end{array}$

Hence, 3.007 + 0.587 + 18.341 = 21.935

(vii) Solving,

$\begin{array}{r} 0.2000 \\ 0.0200 \\ +2.0002 \\ \hline 2.2202 \end{array}$

Hence, 0.2 + 0.02 + 2.0002 = 2.2202

(viii) Solving,

$\begin{array}{r} 6.0800 \\ 60.8000 \\ 0.6080 \\ +0.0608 \\ \hline 67.5488 \end{array}$

Hence, 6.08 + 60.8 + 0.608 + 0.0608 = 67.5488

(ix) Solving,

$\begin{array}{r} 29.0300 \\ 0.0003 \\ 0.3000 \\ +7.2000 \\ \hline 36.5303 \end{array}$

Hence, 29.03 + 0.0003 + 0.3 + 7.2 = 36.5303

(x) Solving,

$\begin{array}{r} 3.4000 \\ 2.0250 \\ 9.3600 \\ +3.6221 \\ \hline 18.4071 \end{array}$

Hence, 3.4 + 2.025 + 9.36 + 3.6221 = 18.4071

Subtract the first number from the second:

(i) 5.4, 9.8

(ii) 0.16, 4.3

(iii) 0.82, 8.6

(iv) 0.07, 8.43

(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

Answer

(i) Solving,

$\begin{array}{r} 9.8 \\ -5.4 \\ \hline 4.4 \end{array}$

Hence, 9.8 - 5.4 = 4.4

(ii) Solving,

$\begin{array}{r} 4.30 \\ -0.16 \\ \hline 4.14 \end{array}$

Hence, 4.3 - 0.16 = 4.14

(iii) Solving,

$\begin{array}{r} 8.60 \\ -0.82 \\ \hline 7.78 \end{array}$

Hence, 8.6 - 0.82 = 7.78

(iv) Solving,

$\begin{array}{r} 8.43 \\ -0.07 \\ \hline 8.36 \end{array}$

Hence, 8.43 - 0.07 = 8.36

(v) Solving,

$\begin{array}{r} 9.425 \\ -2.237 \\ \hline 7.188 \end{array}$

Hence, 9.425 - 2.237 = 7.188

(vi) Solving,

$\begin{array}{r} 59.46 \\ -41.03 \\ \hline 18.43 \end{array}$

Hence, 59.46 - 41.03 = 18.43

(vii) Solving,

$\begin{array}{r} 26.86 \\ -3.92 \\ \hline 22.94 \end{array}$

Hence, 26.86 - 3.92 = 22.94

(viii) Solving,

$\begin{array}{r} 8.50 \\ -4.73 \\ \hline 3.77 \end{array}$

Hence, 8.5 - 4.73 = 3.77

(ix) Solving,

$\begin{array}{r} 36.20 \\ -12.63 \\ \hline 23.57 \end{array}$

Hence, 36.2 - 12.63 = 23.57

(x) Solving,

$\begin{array}{r} 3.710 \\ -0.845 \\ \hline 2.865 \end{array}$

Hence, 3.71 - 0.845 = 2.865

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

Answer

(i) Solving,

28.796 - 13.42 - 2.555 = 28.796 - (13.420 + 2.555)

= 28.796 - 15.975 = 12.821

Hence, 28.796 - 13.42 - 2.555 = 12.821

(ii) Solving,

93.354 - 62.82 - 13.045 = 93.354 - (62.820 + 13.045)

= 93.354 - 75.865 = 17.489

Hence, 93.354 - 62.82 - 13.045 = 17.489

(iii) Solving,

36 - 18.59 - 3.2 = 36.00 - (18.59 + 3.20)

= 36.00 - 21.79 = 14.21

Hence, 36 - 18.59 - 3.2 = 14.21

(iv) Solving,

86 + 16.95 - 3.0042 = (86.0000 + 16.9500) - 3.0042

= 102.9500 - 3.0042 = 99.9458

Hence, 86 + 16.95 - 3.0042 = 99.9458

(v) Solving,

32.8 - 13 - 10.725 + 3.517 = (32.800 + 3.517) - (13.000 + 10.725)

= 36.317 - 23.725 = 12.592

Hence, 32.8 - 13 - 10.725 + 3.517 = 12.592

(vi) Solving,

4000 - 30.51 - 753.101 - 69.43 = 4000.000 - (30.510 + 753.101 + 69.430)

= 4000.000 - 853.041 = 3146.959

Hence, 4000 - 30.51 - 753.101 - 69.43 = 3146.959

(vii) Solving,

0.1835 + 163.2005 - 25.9 - 100 = (0.1835 + 163.2005) - (25.9000 + 100.0000)

= 163.3840 - 125.9000 = 37.484

Hence, 0.1835 + 163.2005 - 25.9 - 100 = 37.484

(viii) Solving,

38.00 - 30 + 200.200 - 0.230 = (38.000 + 200.200) - (30.000 + 0.230)

= 238.200 - 30.230 = 207.97

Hence, 38.00 - 30 + 200.200 - 0.230 = 207.97

(ix) Solving,

555.555 + 55.555 - 5.55 - 0.555 = (555.555 + 55.555) - (5.550 + 0.555)

= 611.110 - 6.105 = 605.005

Hence, 555.555 + 55.555 - 5.55 - 0.555 = 605.005

Find the difference between 6.85 and 0.685.

Answer

Difference = 6.850 - 0.685 = 6.165

Hence, the difference between 6.85 and 0.685 is 6.165.

Take out the sum of 19.38 and 56.025 from 200.111.

Answer

Sum of 19.38 and 56.025:

19.380 + 56.025 = 75.405

Taking out this sum from 200.111:

200.111 - 75.405 = 124.706

Hence, the required result is 124.706.

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

Answer

Adding 13.95 and 1.003:

13.950 + 1.003 = 14.953

Sum of 2.794 and 6.2:

2.794 + 6.200 = 8.994

Subtracting this sum from 14.953:

14.953 - 8.994 = 5.959

Hence, the required result is 5.959.

What should be added to 39.587 to give 80.375?

Answer

Let x be the number to be added.

⇒ 39.587 + x = 80.375

⇒ x = 80.375 - 39.587

⇒ x = 40.788

Hence, 40.788 should be added to 39.587 to give 80.375.

What should be subtracted from 100 to give 19.29?

Answer

Required number = 100.00 - 19.29 = 80.71

Hence, 80.71 should be subtracted from 100 to give 19.29.

What is the excess of 584.29 over 213.95?

Answer

Excess = 584.29 - 213.95 = 370.34

Hence, the excess of 584.29 over 213.95 is 370.34.

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)

Answer

(i) Solving,

(5.4 - 0.8) + (2.97 - 1.462) = 4.6 + (2.970 - 1.462)

= 4.600 + 1.508 = 6.108

Hence, (5.4 - 0.8) + (2.97 - 1.462) = 6.108

(ii) Solving,

(6.25 + 0.36) - (17.2 - 8.97) = 6.61 - (17.20 - 8.97)

= 6.61 - 8.23 = -1.62

Hence, (6.25 + 0.36) - (17.2 - 8.97) = -1.62

(iii) Solving,

9.004 + (3 - 2.462) = 9.004 + (3.000 - 2.462)

= 9.004 + 0.538 = 9.542

Hence, 9.004 + (3 - 2.462) = 9.542

(iv) Solving,

879.4 - (87.94 - 8.794) = 879.4 - (87.940 - 8.794)

= 879.400 - 79.146 = 800.254

Hence, 879.4 - (87.94 - 8.794) = 800.254

What is the excess of 75 over 48.29?

Answer

Excess = 75.00 - 48.29 = 26.71

Hence, the excess of 75 over 48.29 is 26.71.

If A = 237.98 and B = 83.47.

Find: (i) A − B (ii) B − A.

Answer

(i) A - B = 237.98 - 83.47 = 154.51

Hence, A - B = 154.51

(ii) B - A = 83.47 - 237.98 = -154.51

Hence, B - A = -154.51

The cost of one kg of sugar increases from ₹ 28.47 to ₹ 32.65. Find the increase in cost.

Answer

Increase in cost = New cost - Old cost

= ₹ 32.65 - ₹ 28.47 = ₹ 4.18

Hence, the increase in cost is ₹ 4.18.