Decimal Fractions

(i) $3.75 = \frac{375}{100} = \frac{375 \div 25}{100 \div 25} = \frac{15}{4}$

Hence, $3.75 = \frac{15}{4}$

(ii) $0.5 = \frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}$

Hence, $0.5 = \frac{1}{2}$

(iii) $2.04 = \frac{204}{100} = \frac{204 \div 4}{100 \div 4} = \frac{51}{25}$

Hence, $2.04 = \frac{51}{25}$

(iv) $0.65 = \frac{65}{100} = \frac{65 \div 5}{100 \div 5} = \frac{13}{20}$

Hence, $0.65 = \frac{13}{20}$

(v) $2.405 = \frac{2405}{1000} = \frac{2405 \div 5}{1000 \div 5} = \frac{481}{200}$

Hence, $2.405 = \frac{481}{200}$

(vi) $0.085 = \frac{85}{1000} = \frac{85 \div 5}{1000 \div 5} = \frac{17}{200}$

Hence, $0.085 = \frac{17}{200}$

(vii) $8.025 = \frac{8025}{1000} = \frac{8025 \div 25}{1000 \div 25} = \frac{321}{40}$

Hence, $8.025 = \frac{321}{40}$

(i) $2\frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{14}{5} = \frac{14 \times 2}{5 \times 2} = \frac{28}{10} = 2.8$

Hence, $2\frac{4}{5} = 2.8$

(ii) $\frac{79}{100} = 0.79$

Hence, $\frac{79}{100} = 0.79$

(iii) $\frac{37}{10,000} = 0.0037$

Hence, $\frac{37}{10,000} = 0.0037$

(iv) $\frac{7543}{10^4} = \frac{7543}{10000} = 0.7543$

Hence, $\frac{7543}{10^4} = 0.7543$

(v) $\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 0.75$

Hence, $\frac{3}{4} = 0.75$

(vi) $9\frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{48}{5} = \frac{48 \times 2}{5 \times 2} = \frac{96}{10} = 9.6$

Hence, $9\frac{3}{5} = 9.6$

(vii) $8\frac{5}{8} = \frac{8 \times 8 + 5}{8} = \frac{69}{8} = \frac{69 \times 125}{8 \times 125} = \frac{8625}{1000} = 8.625$

Hence, $8\frac{5}{8} = 8.625$

(viii) $5\frac{7}{8} = \frac{5 \times 8 + 7}{8} = \frac{47}{8} = \frac{47 \times 125}{8 \times 125} = \frac{5875}{1000} = 5.875$

Hence, $5\frac{7}{8} = 5.875$

The number of figures that follow the decimal point is called the number of decimal places.

(i) 0.4762 has 4 decimal places.

(ii) 7.00349 has 5 decimal places.

(iii) 8235.403 has 3 decimal places.

(iv) 35.4 has 1 decimal place.

(v) 2.608 has 3 decimal places.

(vi) 0.000879 has 6 decimal places.

(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

Like decimals have the same number of decimal places. We make the number of decimal places equal to the greatest number of decimal places among the given decimals by adding the required number of zeros at the right end (which does not change the value).

(i) The greatest number of decimal places among the given decimals is 4 (in 232.0037). Making each decimal have 4 decimal places:

0.5 = 0.5000
3.62 = 3.6200
43.981 = 43.9810
232.0037 = 232.0037

Hence, the like decimals are 0.5000, 3.6200, 43.9810 and 232.0037.

(ii) The greatest number of decimal places among the given decimals is 5 (in 0.03569). Making each decimal have 5 decimal places:

215.78 = 215.78000
33.0006 = 33.00060
530.3 = 530.30000
0.03569 = 0.03569

Hence, the like decimals are 215.78000, 33.00060, 530.30000 and 0.03569.

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

(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

(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

Difference = 6.850 - 0.685 = 6.165

Hence, the difference between 6.85 and 0.685 is 6.165.

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.

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.

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.

Required number = 100.00 - 19.29 = 80.71

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

Excess = 584.29 - 213.95 = 370.34

Hence, the excess of 584.29 over 213.95 is 370.34.

(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

Excess = 75.00 - 48.29 = 26.71

Hence, the excess of 75 over 48.29 is 26.71.

(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

Increase in cost = New cost - Old cost

= ₹ 32.65 - ₹ 28.47 = ₹ 4.18

Hence, the increase in cost is ₹ 4.18.

(i) On multiplying by 10, shift the decimal point one place to the right.

⇒ 0.87 × 10 = 8.7

Hence, 0.87 × 10 = 8.7

(ii) On multiplying by 100, shift the decimal point two places to the right.

⇒ 2.948 × 100 = 294.8

Hence, 2.948 × 100 = 294.8

(iii) On multiplying by 1000, shift the decimal point three places to the right.

⇒ 6.4 × 1000 = 6400

Hence, 6.4 × 1000 = 6400

(iv) 58 × 4 = 232.

The multiplicand 5.8 has 1 decimal place, so the product has 1 decimal place.

⇒ 5.8 × 4 = 23.2

Hence, 5.8 × 4 = 23.2

(v) 1632 × 28 = 45696.

The multiplicand 16.32 has 2 decimal places, so the product has 2 decimal places.

⇒ 16.32 × 28 = 456.96

Hence, 16.32 × 28 = 456.96

(vi) 5037 × 8 = 40296. The multiplicand 5.037 has 3 decimal places, so the product has 3 decimal places.

⇒ 5.037 × 8 = 40.296

Hence, 5.037 × 8 = 40.296

(vii) 46 × 21 = 966.

The sum of decimal places is 1 + 1 = 2 (4.6 and 2.1 have 1 decimal place each), so the product has 2 decimal places.

⇒ 4.6 × 2.1 = 9.66

Hence, 4.6 × 2.1 = 9.66

(viii) 568 × 64 = 36352. The sum of decimal places is 3 + 1 = 4, so the product has 4 decimal places.

⇒ 0.568 × 6.4 = 3.6352

Hence, 0.568 × 6.4 = 3.6352

On multiplying a decimal number by 10, 100 and 1000, the decimal point shifts to the right, by 1, 2 and 3 places respectively.

(i) Solving,

⇒ 0.5 × 10 = 5

⇒ 0.5 × 100 = 50

⇒ 0.5 × 1000 = 500

Hence, the products are 5, 50 and 500.

(ii) Solving,

⇒ 0.112 × 10 = 1.12

⇒ 0.112 × 100 = 11.2

⇒ 0.112 × 1000 = 112

Hence, the products are 1.12, 11.2 and 112.

(iii) Solving,

⇒ 4.8 × 10 = 48

⇒ 4.8 × 100 = 480

⇒ 4.8 × 1000 = 4800

Hence, the products are 48, 480 and 4800.

(iv) Solving,

⇒ 0.0359 × 10 = 0.359

⇒ 0.0359 × 100 = 3.59

⇒ 0.0359 × 1000 = 35.9

Hence, the products are 0.359, 3.59 and 35.9.

(v) Solving,

⇒ 16.27 × 10 = 162.7

⇒ 16.27 × 100 = 1627

⇒ 16.27 × 1000 = 16270

Hence, the products are 162.7, 1627 and 16270.

(vi) Solving,

⇒ 234.8 × 10 = 2348

⇒ 234.8 × 100 = 23480

⇒ 234.8 × 1000 = 234800

Hence, the products are 2348, 23480 and 234800.

(i) 5897 × 23 = 135631.

Sum of decimal places = 3 + 1 = 4 (3 decimal places in 5.897 and 1 decimal place in 2.3)

⇒ 5.897 × 2.3 = 13.5631

Hence, 5.897 × 2.3 = 13.5631

(ii) 894 × 87 = 77778.

Decimal places = 3.

⇒ 0.894 × 87 = 77.778

Hence, 0.894 × 87 = 77.778

(iii) 1 × 1 = 1.

Sum of decimal places = 2 + 3 = 5.

⇒ 0.01 × 0.001 = 0.00001

Hence, 0.01 × 0.001 = 0.00001

(iv) Solving,

⇒ 0.84 × 2.2 × 4 = (0.84 × 2.2) × 4

= 1.848 × 4 = 7.392

Hence, 0.84 × 2.2 × 4 = 7.392

(v) Solving,

⇒ 4.75 × 0.08 × 3 = (4.75 × 0.08) × 3

= 0.38 × 3 = 1.14

Hence, 4.75 × 0.08 × 3 = 1.14

(vi) Solving,

⇒ 2.4 × 3.5 × 4.8 = (2.4 × 3.5) × 4.8

= 8.4 × 4.8 = 40.32

Hence, 2.4 × 3.5 × 4.8 = 40.32

(vii) Solving,

⇒ 0.8 × 1.2 × 0.25 = (0.8 × 1.2) × 0.25

= 0.96 × 0.25 = 0.24

Hence, 0.8 × 1.2 × 0.25 = 0.24

(viii) Solving,

⇒ 0.3 × 0.03 × 0.003 = (0.3 × 0.03) × 0.003

= 0.009 × 0.003 = 0.000027

Hence, 0.3 × 0.03 × 0.003 = 0.000027

On dividing by 10, shift the decimal point one place to the left.

⇒ 54.9 ÷ 10 = 5.49

Hence, 54.9 ÷ 10 = 5.49

On dividing by 100, shift the decimal point two places to the left.

⇒ 7.8 ÷ 100 = 0.078

Hence, 7.8 ÷ 100 = 0.078

On dividing by 1000, shift the decimal point three places to the left.

⇒ 324.76 ÷ 1000 = 0.32476

Hence, 324.76 ÷ 1000 = 0.32476

By long division,

$$\begin{array}{l} 4\overline{\smash{\big)}\phantom{11}12.8\smash{\big(}}3.2 \\ \phantom{4\smash{\big)},}\underline{-12} \\ \phantom{4\smash{\big)},}\phantom{000..}8 \\ \phantom{4\smash{\big)},}\phantom{00.}\underline{-8} \\ \phantom{4\smash{\big)},}\phantom{000.}\times \end{array}$$

Hence, 12.8 ÷ 4 = 3.2

By long division,

$$\begin{array}{l} 9\overline{\smash{\big)}\phantom{11}27.918\smash{\big(}}3.102 \\ \phantom{9\smash{\big)},}\underline{-27} \\ \phantom{9\smash{\big)},}\phantom{0000}9 \\ \phantom{9\smash{\big)},}\phantom{00.}\underline{-9} \\ \phantom{9\smash{\big)},}\phantom{000.11}18 \\ \phantom{9\smash{\big)},}\phantom{0000}\underline{-18} \\ \phantom{9\smash{\big)},}\phantom{00000.}\times \end{array}$$

Hence, 27.918 ÷ 9 = 3.102

By long division,

$$\begin{array}{l} 8\overline{\smash{\big)}\phantom{000}4.672\smash{\big(}}0.584 \\ \phantom{8\smash{\big)},}\phantom{}\underline{-40} \\ \phantom{8\smash{\big)},}\phantom{000.}67 \\ \phantom{8\smash{\big)},}\phantom{00}\underline{-64} \\ \phantom{8\smash{\big)},}\phantom{0000..}32 \\ \phantom{8\smash{\big)},}\phantom{000.}\underline{-32} \\ \phantom{8\smash{\big)},}\phantom{00000}\times \end{array}$$

Hence, 4.672 ÷ 8 = 0.584

Shift the decimal point of both dividend and divisor by 1 place to make the divisor a whole number.

$4.32 \div 1.2 = \frac{43.2}{12}$

By long division,

$$\begin{array}{l} 12\overline{\smash{\big)}\phantom{0.}43.2\smash{\big(}}3.6 \\ \phantom{12\smash{\big)},}\underline{-36} \\ \phantom{12\smash{\big)},}\phantom{00.}72 \\ \phantom{12\smash{\big)},}\phantom{0}\underline{-72} \\ \phantom{12\smash{\big)},}\phantom{00.}\times \end{array}$$

Hence, 4.32 ÷ 1.2 = 3.6

Shift the decimal point of both dividend and divisor by 1 place to make the divisor a whole number.

$7.644 \div 1.4 = \frac{76.44}{14}$

By long division,

$$\begin{array}{l} 14\overline{\smash{\big)}\phantom{00}76.44\smash{\big(}}5.46 \\ \phantom{14\smash{\big)},}\underline{-70} \\ \phantom{14\smash{\big)},}\phantom{000}64 \\ \phantom{14\smash{\big)},}\phantom{0.}\underline{-56} \\ \phantom{14\smash{\big)},}\phantom{0000.}84 \\ \phantom{14\smash{\big)},}\phantom{000}\underline{-84} \\ \phantom{14\smash{\big)},}\phantom{0000.}\times \end{array}$$

Hence, 7.644 ÷ 1.4 = 5.46

Shift the decimal point of both dividend and divisor by 2 places to make the divisor a whole number.

$4.8432 \div 0.08 = \frac{484.32}{8}$

By long division,

$$\begin{array}{l} 8\overline{\smash{\big)}\phantom{00.}484.32\smash{\big(}}60.54 \\ \phantom{8\smash{\big)},}\underline{-48} \\ \phantom{8\smash{\big)},}\phantom{000..}43 \\ \phantom{8\smash{\big)},}\phantom{00.}\underline{-40} \\ \phantom{8\smash{\big)},}\phantom{0000..}32 \\ \phantom{8\smash{\big)},}\phantom{000.}\underline{-32} \\ \phantom{8\smash{\big)},}\phantom{00000}\times \end{array}$$

Hence, 4.8432 ÷ 0.08 = 60.54

On dividing a decimal number by 10, 100, 1000, 10000, the decimal point shifts to the left, by 1, 2, 3 and 4 places respectively.

Solving,

⇒ 2.1 ÷ 10 = 0.21

⇒ 2.1 ÷ 100 = 0.021

⇒ 2.1 ÷ 1000 = 0.0021

⇒ 2.1 ÷ 10000 = 0.00021

Hence, the quotients are 0.21, 0.021, 0.0021 and 0.00021.

On dividing a decimal number by 10, 100, 1000, 10000, the decimal point shifts to the left, by 1, 2, 3 and 4 places respectively.

Solving,

⇒ 8.64 ÷ 10 = 0.864

⇒ 8.64 ÷ 100 = 0.0864

⇒ 8.64 ÷ 1000 = 0.00864

⇒ 8.64 ÷ 10000 = 0.000864

Hence, the quotients are 0.864, 0.0864, 0.00864 and 0.000864.

On dividing a decimal number by 10, 100, 1000, 10000, the decimal point shifts to the left, by 1, 2, 3 and 4 places respectively.

Solving,

⇒ 5.01 ÷ 10 = 0.501

⇒ 5.01 ÷ 100 = 0.0501

⇒ 5.01 ÷ 1000 = 0.00501

⇒ 5.01 ÷ 10000 = 0.000501

Hence, the quotients are 0.501, 0.0501, 0.00501 and 0.000501.

On dividing a decimal number by 10, 100, 1000, 10000, the decimal point shifts to the left, by 1, 2, 3 and 4 places respectively.

Solving,

⇒ 0.0906 ÷ 10 = 0.00906

⇒ 0.0906 ÷ 100 = 0.000906

⇒ 0.0906 ÷ 1000 = 0.0000906

⇒ 0.0906 ÷ 10000 = 0.00000906

Hence, the quotients are 0.00906, 0.000906, 0.0000906 and 0.00000906.

On dividing a decimal number by 10, 100, 1000, 10000, the decimal point shifts to the left, by 1, 2, 3 and 4 places respectively.

Solving,

⇒ 0.125 ÷ 10 = 0.0125

⇒ 0.125 ÷ 100 = 0.00125

⇒ 0.125 ÷ 1000 = 0.000125

⇒ 0.125 ÷ 10000 = 0.0000125

Hence, the quotients are 0.0125, 0.00125, 0.000125 and 0.0000125.

On dividing a decimal number by 10, 100, 1000, 10000, the decimal point shifts to the left, by 1, 2, 3 and 4 places respectively.

Solving,

⇒ 111.11 ÷ 10 = 11.111

⇒ 111.11 ÷ 100 = 1.1111

⇒ 111.11 ÷ 1000 = 0.11111

⇒ 111.11 ÷ 10000 = 0.011111

Hence, the quotients are 11.111, 1.1111, 0.11111 and 0.011111.

By long division,

$$\begin{array}{l} 5\overline{\smash{\big)}\phantom{00.}9.75\smash{\big(}}1.95 \\ \phantom{5\smash{\big)},}\underline{-5} \\ \phantom{5\smash{\big)},}\phantom{00}47 \\ \phantom{5\smash{\big)},}\phantom{.}\underline{-45} \\ \phantom{5\smash{\big)},}\phantom{000.}25 \\ \phantom{5\smash{\big)},}\phantom{00}\underline{-25} \\ \phantom{5\smash{\big)},}\phantom{0000}\times \end{array}$$

Hence, 9.75 ÷ 5 = 1.95

By long division,

$$\begin{array}{l} 4\overline{\smash{\big)}\phantom{00}4.4064\smash{\big(}}1.1016 \\ \phantom{4\smash{\big)},}\underline{-4} \\ \phantom{4\smash{\big)},}\phantom{000}4 \\ \phantom{4\smash{\big)},}\phantom{0.}\underline{-4} \\ \phantom{000000.}06 \\ \phantom{+))}\phantom{00..}\underline{-4} \\ \phantom{+))}\phantom{0000.}24 \\ \phantom{+))}\phantom{00..}\underline{-24} \\ \phantom{4\smash{\big)},}\phantom{00000.}\times \end{array}$$

Hence, 4.4064 ÷ 4 = 1.1016

By long division,

$$\begin{array}{l} 30\overline{\smash{\big)}\phantom{00.}27.690\smash{\big(}}0.923 \\ \phantom{((()}\phantom{.}\underline{-270} \\ \phantom{30\smash{\big)},}\phantom{0000.}69 \\ \phantom{30\smash{\big)},}\phantom{000}\underline{-60} \\ \phantom{30\smash{\big)},}\phantom{00000.}90 \\ \phantom{30\smash{\big)},}\phantom{000..}\underline{-90} \\ \phantom{30\smash{\big)},}\phantom{000000}\times \end{array}$$

Hence, 27.69 ÷ 30 = 0.923

By long division,

$$\begin{array}{l} 25\overline{\smash{\big)}\phantom{0...}19.25\smash{\big(}}0.77 \\ \phantom{25\smash{\big)},}\phantom{}\underline{-175} \\ \phantom{25\smash{\big)},}\phantom{000.}175 \\ \phantom{25\smash{\big)},}\phantom{00}\underline{-175} \\ \phantom{25\smash{\big)},}\phantom{0000.}\times \end{array}$$

Hence, 19.25 ÷ 25 = 0.77

By long division,

$$\begin{array}{l} 16\overline{\smash{\big)}\phantom{00.}20.64\smash{\big(}}1.29 \\ \phantom{16\smash{\big)},}\underline{-16} \\ \phantom{16\smash{\big)},}\phantom{000}46 \\ \phantom{16\smash{\big)},}\phantom{0.}\underline{-32} \\ \phantom{16\smash{\big)},}\phantom{000}144 \\ \phantom{16\smash{\big)},}\phantom{0.}\underline{-144} \\ \phantom{16\smash{\big)},}\phantom{0000}\times \end{array}$$

Hence, 20.64 ÷ 16 = 1.29

By long division,

$$\begin{array}{l} 9\overline{\smash{\big)}\phantom{00.}3.204\smash{\big(}}0.356 \\ \phantom{9\smash{\big)},}\phantom{..}\underline{-27} \\ \phantom{9\smash{\big)},}\phantom{000.}50 \\ \phantom{9\smash{\big)},}\phantom{00}\underline{-45} \\ \phantom{9\smash{\big)},}\phantom{0000.}54 \\ \phantom{9\smash{\big)},}\phantom{000}\underline{-54} \\ \phantom{9\smash{\big)},}\phantom{0000.}\times \end{array}$$

Hence, 3.204 ÷ 9 = 0.356

By long division,

$$\begin{array}{l} 25\overline{\smash{\big)}\phantom{00}0.125\smash{\big(}}0.005 \\ \phantom{25\smash{\big)},}\phantom{0.}\underline{-125} \\ \phantom{25\smash{\big)},}\phantom{0000}\times \end{array}$$

Hence, 0.125 ÷ 25 = 0.005

By long division,

$$\begin{array}{l} 72\overline{\smash{\big)}\phantom{00}0.14616\smash{\big(}}0.00203 \\ \phantom{72\smash{\big)},}\phantom{0.}\underline{-144} \\ \phantom{72\smash{\big)},}\phantom{0000..}216 \\ \phantom{72\smash{\big)},}\phantom{000.}\underline{-216} \\ \phantom{72\smash{\big)},}\phantom{00000..}\times \end{array}$$

Hence, 0.14616 ÷ 72 = 0.00203

By long division,

$$\begin{array}{l} 1300\overline{\smash{\big)}\phantom{000..}0.622700\smash{\big(}}0.000479 \\ \phantom{1300\smash{\big)},}\phantom{000.}\underline{-5200} \\ \phantom{1300\smash{\big)},}\phantom{00000}10270 \\ \phantom{1300\smash{\big)},}\phantom{0000.}\underline{-9100} \\ \phantom{1300\smash{\big)},}\phantom{00000..}11700 \\ \phantom{1300\smash{\big)},}\phantom{0000.}\underline{-11700} \\ \phantom{1300\smash{\big)},}\phantom{00000000}\times \end{array}$$

Hence, 0.6227 ÷ 1300 = 0.000479

Shift the decimal point of both dividend and divisor by 3 places to make the divisor a whole number.

$257.894 \div 0.169 = \frac{257894}{169}$

By long division,

$$\begin{array}{l} 169\overline{\smash{\big)}\phantom{00.}257894\smash{\big(}}1526 \\ \phantom{169\smash{\big)},}\underline{-169} \\ \phantom{169\smash{\big)},}\phantom{00.}888 \\ \phantom{169\smash{\big)},}\phantom{0}\underline{-845} \\ \phantom{169\smash{\big)},}\phantom{0.00}439 \\ \phantom{169\smash{\big)},}\phantom{00}\underline{-338} \\ \phantom{169\smash{\big)},}\phantom{000.}1014 \\ \phantom{169\smash{\big)},}\phantom{00}\underline{-1014} \\ \phantom{169\smash{\big)},}\phantom{00000}\times \end{array}$$

Hence, 257.894 ÷ 0.169 = 1526

$6.3 \div (0.3)^2 = 6.3 \div 0.09 = \frac{630}{9}$

By long division,

$$\begin{array}{l} 9\overline{\smash{\big)}\phantom{00}630\smash{\big(}}70 \\ \phantom{9\smash{\big)},}\underline{-63} \\ \phantom{9\smash{\big)},}\phantom{0.}\times \end{array}$$

Hence, 6.3 ÷ (0.3)² = 70

(i) Solving,

⇒ 4.3 × 0.52 × 0.3 = (4.3 × 0.52) × 0.3

= 2.236 × 0.3 = 0.6708

Hence, 4.3 × 0.52 × 0.3 = 0.6708

(ii) Solving,

⇒ 3.2 × 2.5 × 0.7 = (3.2 × 2.5) × 0.7

= 8 × 0.7 = 5.6

Hence, 3.2 × 2.5 × 0.7 = 5.6

(iii) Solving,

⇒ 0.8 × 1.5 × 0.6 = (0.8 × 1.5) × 0.6

= 1.2 × 0.6 = 0.72

Hence, 0.8 × 1.5 × 0.6 = 0.72

(iv) Solving,

⇒ 0.3 × 0.3 × 0.3 = (0.3 × 0.3) × 0.3

= 0.09 × 0.3 = 0.027

Hence, 0.3 × 0.3 × 0.3 = 0.027

(v) Solving,

⇒ 1.2 × 1.2 × 0.4 = (1.2 × 1.2) × 0.4

= 1.44 × 0.4 = 0.576

Hence, 1.2 × 1.2 × 0.4 = 0.576

(vi) Solving,

⇒ 0.4 × 0.04 × 0.004 = (0.4 × 0.04) × 0.004

= 0.016 × 0.004 = 0.000064

Hence, 0.4 × 0.04 × 0.004 = 0.000064

(vii) Solving,

⇒ 0.5 × 0.6 × 0.7 = (0.5 × 0.6) × 0.7

= 0.3 × 0.7 = 0.21

Hence, 0.5 × 0.6 × 0.7 = 0.21

(viii) Solving,

⇒ 0.5 × 0.06 × 0.007 = (0.5 × 0.06) × 0.007

= 0.03 × 0.007 = 0.00021

Hence, 0.5 × 0.06 × 0.007 = 0.00021

(i) (0.9)² = 0.9 × 0.9 = 0.81

Hence, (0.9)² = 0.81

(ii) Solving,

⇒ (0.6)² × 0.5 = (0.6 × 0.6) × 0.5

= 0.36 × 0.5 = 0.18

Hence, (0.6)² × 0.5 = 0.18

(iii) Solving,

⇒ 0.3 × (0.5)² = 0.3 × (0.5 × 0.5)

= 0.3 × 0.25 = 0.075

Hence, 0.3 × (0.5)² = 0.075

(iv) (0.4)³ = 0.4 × 0.4 × 0.4 = 0.064

Hence, (0.4)³ = 0.064

(v) Solving,

⇒ (0.2)³ × 5 = (0.2 × 0.2 × 0.2) × 5

= 0.008 × 5 = 0.04

Hence, (0.2)³ × 5 = 0.04

(vi) Solving,

⇒ (0.2)³ × 0.05 = (0.2 × 0.2 × 0.2) × 0.05

= 0.008 × 0.05 = 0.0004

Hence, (0.2)³ × 0.05 = 0.0004

Cost of wheat = Rate per kg × Weight

= ₹ 12.80 × 36.75 = ₹ 470.40

Hence, the cost of 36.75 kg wheat is ₹ 470.40.

Cost of 16 pens = Cost of one pen × 16

= ₹ 56.15 × 16 = ₹ 898.40

Hence, the cost of 16 pens is ₹ 898.40.

Shift the decimal point of both numbers by 2 places.

$0.0072 \div 0.06 = \frac{0.72}{6}$

By long division,

$$\begin{array}{l} 6\overline{\smash{\big)}\phantom{0..}0.72\smash{\big(}}0.12 \\ \phantom{6\smash{\big)},}\phantom{0.}\underline{-6} \\ \phantom{6\smash{\big)},}\phantom{000}12 \\ \phantom{6\smash{\big)},}\phantom{0.}\underline{-12} \\ \phantom{6\smash{\big)},}\phantom{00.0}\times \end{array}$$

Hence, 0.0072 ÷ 0.06 = 0.12

Shift the decimal point of both numbers by 1 place.

$0.621 \div 0.3 = \frac{6.21}{3}$

By long division,

$$\begin{array}{l} 3\overline{\smash{\big)}\phantom{00}6.21\smash{\big(}}2.07 \\ \phantom{3\smash{\big)},}\underline{-6} \\ \phantom{3\smash{\big)},}\phantom{000}21 \\ \phantom{3\smash{\big)},}\phantom{0.}\underline{-21} \\ \phantom{3\smash{\big)},}\phantom{000}\times \end{array}$$

Hence, 0.621 ÷ 0.3 = 2.07

Shift the decimal point of both numbers by 3 places.

$0.0532 \div 0.005 = \frac{53.2}{5}$

By long division,

$$\begin{array}{l} 5\overline{\smash{\big)}\phantom{00}53.20\smash{\big(}}10.64 \\ \phantom{5\smash{\big)},}\underline{-5} \\ \phantom{+}\phantom{000.}32 \\ \phantom{+}\phantom{00}\underline{-30} \\ \phantom{+}\phantom{0000.}20 \\ \phantom{+}\phantom{000}\underline{-20} \\ \phantom{+}\phantom{0000.}\times \end{array}$$

Hence, 0.0532 ÷ 0.005 = 10.64

Shift the decimal point of both numbers by 2 places.

$0.01162 \div 0.14 = \frac{1.162}{14}$

By long division,

$$\begin{array}{l} 14\overline{\smash{\big)}\phantom{00.}1.162\smash{\big(}}0.083 \\ \phantom{14\smash{\big)},}\phantom{.}\underline{-112} \\ \phantom{14\smash{\big)},}\phantom{0000.}42 \\ \phantom{14\smash{\big)},}\phantom{000}\underline{-42} \\ \phantom{14\smash{\big)},}\phantom{00000}\times \end{array}$$

Hence, 0.01162 ÷ 0.14 = 0.083

(7.5 × 40.4) ÷ 25 = 303 ÷ 25

By long division,

$$\begin{array}{l} 25\overline{\smash{\big)}\phantom{00.}303.00\smash{\big(}}12.12 \\ \phantom{25\smash{\big)},}\underline{-25} \\ \phantom{25\smash{\big)},}\phantom{00.}53 \\ \phantom{25\smash{\big)},}\phantom{0}\underline{-50} \\ \phantom{25\smash{\big)},}\phantom{0000.}30 \\ \phantom{25\smash{\big)},}\phantom{00..}\underline{-25} \\ \phantom{25\smash{\big)},}\phantom{00000.}50 \\ \phantom{25\smash{\big)},}\phantom{0000}\underline{-50} \\ \phantom{25\smash{\big)},}\phantom{00000.}\times \end{array}$$

Hence, (7.5 × 40.4) ÷ 25 = 12.12

$2.1 \div (0.1 \times 0.1) = 2.1 \div 0.01 = \frac{210}{1} = 210$

Hence, 2.1 ÷ (0.1 × 0.1) = 210

Weight of each article = Total weight ÷ Number of articles

= 31.50 ÷ 15 = 2.1 kg

Hence, the weight of each article is 2.1 kg.

Other number = Product ÷ One number

$= 211.2 \div 16.5 = \frac{2112}{165} = 12.8$

Hence, the other number is 12.8.

One dozen = 12 articles.

Cost of each article = Total cost ÷ Number of articles

= ₹ 45.96 ÷ 12 = ₹ 3.83

Hence, the cost of each article is ₹ 3.83.

By long division,

$$\begin{array}{l} 8\overline{\smash{\big)}\phantom{00.}3.000\smash{\big(}}0.375 \\ \phantom{8\smash{\big)},}\phantom{..}\underline{-24} \\ \phantom{8\smash{\big)},}\phantom{000.}60 \\ \phantom{8\smash{\big)},}\phantom{00}\underline{-56} \\ \phantom{8\smash{\big)},}\phantom{0000.}40 \\ \phantom{8\smash{\big)},}\phantom{000}\underline{-40} \\ \phantom{8\smash{\big)},}\phantom{00000}\times \end{array}$$

The remainder becomes zero, so the division ends after a finite number of steps and 3 ÷ 8 = 0.375.

Hence, it is a Terminating decimal.

By long division,

$$\begin{array}{l} 3\overline{\smash{\big)}\phantom{00}8.000\smash{\big(}}2.666\ldots \\ \phantom{3\smash{\big)},}\underline{-6} \\ \phantom{+}\phantom{00.}20 \\ \phantom{+}\phantom{..}\underline{-18} \\ \phantom{+}\phantom{000.}20 \\ \phantom{+}\phantom{0..}\underline{-18} \\ \phantom{+}\phantom{0000.}20 \\ \phantom{+}\phantom{000}\underline{-18} \\ \phantom{+}\phantom{00000.}2 \\ \phantom{+}\phantom{00000}\ \vdots \end{array}$$

The remainder never becomes zero, so the division never ends and 8 ÷ 3 = 2.666….

Hence, it is a Non-terminating decimal.

By long division,

$$\begin{array}{l} 5\overline{\smash{\big)}\phantom{0..}6.0\smash{\big(}}1.2 \\ \phantom{5\smash{\big)}.}\underline{-5} \\ \phantom{5\smash{\big)},}\phantom{00}10 \\ \phantom{5\smash{\big)},}\phantom{.}\underline{-10} \\ \phantom{5\smash{\big)},}\phantom{00}\times \end{array}$$

The remainder becomes zero, so the division ends after a finite number of steps and 6 ÷ 5 = 1.2.

Hence, it is a Terminating decimal.

By long division,

$$\begin{array}{l} 6\overline{\smash{\big)}\phantom{000}5.0000\smash{\big(}}0.8333\ldots \\ \phantom{6\smash{\big)},}\phantom{0.}\underline{-48} \\ \phantom{6\smash{\big)},}\phantom{0000}20 \\ \phantom{6\smash{\big)},}\phantom{00.}\underline{-18} \\ \phantom{6\smash{\big)},}\phantom{0000..}20 \\ \phantom{6\smash{\big)},}\phantom{000.}\underline{-18} \\ \phantom{6\smash{\big)},}\phantom{0000.0.}20 \\ \phantom{6\smash{\big)},}\phantom{0000.}\underline{-18} \\ \phantom{6\smash{\big)},}\phantom{000000..}2 \\ \phantom{6\smash{\big)},}\phantom{000000.}\ \vdots \end{array}$$

The remainder never becomes zero, so the division never ends and 5 ÷ 6 = 0.8333….

Hence, it is a Non-terminating decimal.

By long division,

$$\begin{array}{l} 4\overline{\smash{\big)}\phantom{00}12.500\smash{\big(}}3.125 \\ \phantom{4\smash{\big)},}\underline{-12} \\ \phantom{4\smash{\big)},}\phantom{000.}5 \\ \phantom{4\smash{\big)},}\phantom{00}\underline{-4} \\ \phantom{4\smash{\big)},}\phantom{0000}10 \\ \phantom{4\smash{\big)},}\phantom{000.}\underline{-8} \\ \phantom{4\smash{\big)},}\phantom{00000.}20 \\ \phantom{4\smash{\big)},}\phantom{0000}\underline{-20} \\ \phantom{4\smash{\big)},}\phantom{000000}\times \end{array}$$

The remainder becomes zero, so the division ends after a finite number of steps and 12.5 ÷ 4 = 3.125.

Hence, it is a Terminating decimal.

$23 \div 0.7 = \frac{230}{7}$

By long division,

$$\begin{array}{l} 7\overline{\smash{\big)}\phantom{00}230.000\smash{\big(}}32.857\ldots \\ \phantom{7\smash{\big)},}\underline{-21} \\ \phantom{7\smash{\big)},}\phantom{00.}20 \\ \phantom{7\smash{\big)},}\phantom{0}\underline{-14} \\ \phantom{7\smash{\big)},}\phantom{000.}60 \\ \phantom{7\smash{\big)},}\phantom{00}\underline{-56} \\ \phantom{7\smash{\big)},}\phantom{0000.}40 \\ \phantom{7\smash{\big)},}\phantom{000}\underline{-35} \\ \phantom{7\smash{\big)},}\phantom{00000.}50 \\ \phantom{7\smash{\big)},}\phantom{000..}\underline{-49} \\ \phantom{7\smash{\big)},}\phantom{0000000}1 \\ \phantom{7\smash{\big)},}\phantom{000000}\ \vdots \end{array}$$

The remainder never becomes zero, so the division never ends and 23 ÷ 0.7 = 32.857….

Hence, it is a Non-terminating decimal.

By long division,

$$\begin{array}{l} 9\overline{\smash{\big)}\phantom{00}42.000\smash{\big(}}4.666\ldots \\ \phantom{9\smash{\big)},}\underline{-36} \\ \phantom{9\smash{\big)},}\phantom{00.}60 \\ \phantom{9\smash{\big)},}\phantom{0}\underline{-54} \\ \phantom{9\smash{\big)},}\phantom{0000}60 \\ \phantom{9\smash{\big)},}\phantom{00.}\underline{-54} \\ \phantom{9\smash{\big)},}\phantom{00000.}60 \\ \phantom{9\smash{\big)},}\phantom{0000}\underline{-54} \\ \phantom{9\smash{\big)},}\phantom{000000.}6 \\ \phantom{9\smash{\big)},}\phantom{00000}\ \vdots \end{array}$$

The remainder never becomes zero, so the division never ends and 42 ÷ 9 = 4.666….

Hence, it is a Non-terminating decimal.

$0.56 \div 0.11 = \frac{56}{11}$

By long division,

$$\begin{array}{l} 11\overline{\smash{\big)}\phantom{00}56.0000\smash{\big(}}5.0909\ldots \\ \phantom{11\smash{\big)},}\underline{-55} \\ \phantom{11\smash{\big)},}\phantom{000}100 \\ \phantom{11\smash{\big)},}\phantom{00.}\underline{-99} \\ \phantom{11\smash{\big)},}\phantom{00000.}100 \\ \phantom{11\smash{\big)},}\phantom{00000}\underline{-99} \\ \phantom{11\smash{\big)},}\phantom{0000000.}1 \\ \phantom{11\smash{\big)},}\phantom{000000.}\ \vdots \end{array}$$

The remainder never becomes zero, so the division never ends and 0.56 ÷ 0.11 = 5.0909….

Hence, it is a Non-terminating decimal.

Total weight = Weight of one object × Number of objects

= 3.06 × 48 = 146.88 kg

Hence, the total weight of 48 objects is 146.88 kg.

Cost of cloth = Rate per metre × Length

= ₹ 112.50 × 17.5 = ₹ 1968.75

Hence, the cost of 17.5 m cloth is ₹ 1968.75.

Cost of oil = Cost per kg × Weight

= ₹ 73.40 × 9.75 = ₹ 715.65

Hence, the cost of 9.75 kg of oil is ₹ 715.65.

Weight of each object = Total weight ÷ Number of objects

= 51.2 ÷ 8

= 6.4 kg

Hence, the weight of each object is 6.4 kg.

Given,

Cost of 18.5 m of cloth = ₹ 666

Cost of 1 m cloth = ₹ 666 ÷ 18.5 = ₹ 36

Cost of 3.8 m cloth = ₹ 36 × 3.8 = ₹ 136.80

Hence, the cost of 3.8 m cloth is ₹ 136.80.

(i) Solving,

0.5 of ₹ 7.60 + 1.62 of ₹ 30 = (0.5 × 7.60) + (1.62 × 30)

= 3.80 + 48.60 = ₹ 52.40

Hence, the value is ₹ 52.40.

(ii) Solving,

2.3 of 7.3 kg + 0.9 of 0.48 kg = (2.3 × 7.3) + (0.9 × 0.48)

= 16.79 + 0.432 = 17.222 kg

Hence, the value is 17.222 kg.

(iii) Solving,

6.25 of 8.4 - 4.7 of 3.24 = (6.25 × 8.4) - (4.7 × 3.24)

= 52.5 - 15.228 = 37.272

Hence, the value is 37.272.

(iv) Solving,

0.98 of 235 - 0.09 of 3.2 = (0.98 × 235) - (0.09 × 3.2)

= 230.3 - 0.288 = 230.012

Hence, the value is 230.012.

Following the order of operations (here 'of' is performed before ÷ and ×):

(i) Solving,

5.6 - 1.5 of 3.4 = 5.6 - (1.5 × 3.4)

= 5.6 - 5.1 = 0.5

Hence, 5.6 - 1.5 of 3.4 = 0.5

(ii) Solving,

4.8 ÷ 0.04 of 5 = 4.8 ÷ (0.04 × 5)

$= 4.8 \div 0.2 = \frac{48}{2} = 24$

Hence, 4.8 ÷ 0.04 of 5 = 24

(iii) Solving,

0.72 of 80 ÷ 0.2 = (0.72 × 80) ÷ 0.2

$= 57.6 \div 0.2 = \frac{576}{2} = 288$

Hence, 0.72 of 80 ÷ 0.2 = 288

(iv) Solving,

0.72 ÷ 80 of 0.2 = 0.72 ÷ (80 × 0.2)

= 0.72 ÷ 16 = 0.045

Hence, 0.72 ÷ 80 of 0.2 = 0.045

(v) Solving,

6.45 ÷ (3.9 - 1.75) = 6.45 ÷ 2.15

$= \frac{645}{215} = 3$

Hence, 6.45 ÷ (3.9 - 1.75) = 3

(vi) Solving,

0.12 of (0.104 - 0.02) + 0.36 × 0.5 = 0.12 × 0.084 + 0.18

= 0.01008 + 0.18 = 0.19008

Hence, 0.12 of (0.104 - 0.02) + 0.36 × 0.5 = 0.19008

Converting to like decimals: 5.038 and 5.300.

Comparing the digits after the decimal point, 300 > 038, so 5.3 > 5.038.

∴ 5.3 is greater.

Hence, Option 2 is the correct option.

Shyama bought 5 kg 300 g = 5.300 kg apples

Shyama bought 3 kg 250 g = 3.250 kg mangoes

Sarla bought 4 kg 800 g = 4.800 kg oranges

Sarla bought 4 kg 150 g = 4.150 kg bananas

Total weight of fruits bought by Shyama = 5.300 + 3.250 = 8.550 kg

Total weight of fruits bought by Sarla = 4.800 + 4.150 = 8.950 kg

Since 8.950 > 8.550, Sarla bought more fruits.

Hence, Option 2 is the correct option.

Cream in 2 kg milk = 0.315 kg

Cream in 1 kg milk $= \frac{0.315}{2}$ kg

Cream in 20 kg milk $= \frac{0.315}{2} \times 20 = 0.315 \times 10 = 3.15$ kg

Hence, Option 3 is the correct option.

Distance covered in 4.8 hours = 86.4 km

Distance covered in 1 hour $= \frac{86.4}{4.8}$ km

Hence, Option 2 is the correct option.

Seven and 7 thousandth $= 7 + \frac{7}{1000} = 7 + 0.007 = 7.007$

Hence, Option 4 is the correct option.

$56.56 \div 1.4 = \frac{565.6}{14} = 40.4$

Hence, Option 2 is the correct option.

Solving,

$$\begin{aligned}\Rightarrow \left(2 + \frac{1}{2}\right) \div \frac{3}{5} \\[1em] \Rightarrow \frac{5}{2} \div \frac{3}{5} \\[1em] \Rightarrow \frac{5}{2} \times \frac{5}{3} \\[1em] \Rightarrow \frac{25}{6} \\[1em] \Rightarrow 4\frac{1}{6}\end{aligned}$$

Hence, Option 1 is the correct option.

Cost of 2 pens = 2 × 5.30 = ₹ 10.60

Cost of 4 notebooks = 4 × 20.50 = ₹ 82.00

Total cost = 10.60 + 82.00 = ₹ 92.60

Hence, Option 3 is the correct option.

Following the order of operations, division is performed before addition:

$$\begin{aligned}\Rightarrow 2.5 + 3.8 \div 0.02 \\[1em] \Rightarrow 2.5 + \frac{3.8}{0.02} \\[1em] \Rightarrow 2.5 + \frac{380}{2} \\[1em] \Rightarrow 2.5 + 190 \\[1em] \Rightarrow 192.5\end{aligned}$$

Hence, Option 2 is the correct option.

Let the required number be $x$.

$$\begin{aligned}\Rightarrow 0.0001 \div x = 0.01 \\[1em] \Rightarrow \frac{0.0001}{x} = 0.01 \\[1em] \Rightarrow x = \frac{0.0001}{0.01} \\[1em] \Rightarrow x =\frac{100}{10000} \\[1em] \Rightarrow x = \frac{1}{100} = 0.01\end{aligned}$$

Hence, Option 4 is the correct option.

Solving,

$$\begin{aligned}\Rightarrow 3\frac{1}{5} \times \left(\frac{1}{2} + \frac{3}{8}\right) \div \frac{21}{40} \\[1em] \Rightarrow \frac{16}{5} \times \left(\frac{4}{8} + \frac{3}{8}\right) \div \frac{21}{40} \\[1em] \Rightarrow \frac{16}{5} \times \frac{7}{8} \div \frac{21}{40} \\[1em] \Rightarrow \frac{14}{5} \times \frac{40}{21} \\[1em] \Rightarrow \frac{16}{3} = 5\frac{1}{3}\end{aligned}$$

Hence, Option 3 is the correct option.

Comparing the numbers: 5.80 > 1.92 > 1.87 > 0.95.

So the descending order is 5.80, 1.92, 1.87 and 0.95.

Hence, Option 2 is the correct option.

Solving,

$$\begin{aligned}\Rightarrow 3 - \frac{1}{4} \text{ of } (15.8 - 3) \\[1em] \Rightarrow 3 - \frac{1}{4} \text{ of } 12.8 \\[1em] \Rightarrow 3 - \frac{1}{4} \times 12.8 \\[1em] \Rightarrow 3 - 3.2 = -0.2\end{aligned}$$

Hence, Option 3 is the correct option.

In Statement 1, 0.05 = 0.050 = 0.0500, but 0.005 = 0.00500, and 0.05 ≠ 0.005 (since 0.05 is five hundredths while 0.005 is five thousandths). So Statement 1 is false.

Statement 2 correctly states that adding zeros at the right end of a decimal number does not change its value, so Statement 2 is true.

∴ Statement 1 is false, and statement 2 is true.

Hence, Option 4 is the correct option.

For the Assertion:

$6.25 = 6 + 0.25 = 6 + \frac{25}{100} = 6 + \frac{1}{4} = 6\frac{1}{4}$

In the fraction $6\frac{1}{4}$, the denominator (4) is a natural number and cannot be expressed as 10ⁿ, n∈N. So the Assertion (A) is true.

The Reason correctly states the condition for a fraction to be a vulgar fraction, so the Reason (R) is true.

∴ Both A and R are true.

Hence, Option 3 is the correct option.

For the Assertion, the other number $= 17.55 \div 6.5 = \frac{175.5}{65} = 2.7$. So the Assertion (A) is true.

The Reason states a true general fact that in division of decimal numbers, the dividend is not always exactly divisible. So the Reason (R) is true.

∴ Both A and R are true.

Hence, Option 3 is the correct option.

For the Assertion:

$3.10 \div (0.1 \times 0.1) = 3.10 \div 0.01 = \frac{310}{1} = 310$

Since the result is 310 and not 3.1, the Assertion (A) is false.

The Reason correctly states that in division of a decimal number by 10ⁿ, the decimal point is shifted to the left by n places, so the Reason (R) is true.

∴ A is false, R is true.

Hence, Option 2 is the correct option.

For the Assertion, 9, 9.56, 9.2 and 9.005 are indeed unlike decimals (they have different numbers of decimal places). However, addition can still be performed by converting them into like decimals (9.000, 9.560, 9.200, 9.005). So the claim that "addition can't be performed" is wrong, and the Assertion (A) is false.

The Reason correctly states that a whole number can be expressed as a decimal number by placing a decimal point after the units digit and adding as many zeros to its right as required. So, the Reason (R) is true.

∴ A is false, R is true.

Hence, Option 2 is the correct option.