Decimal Fractions — Exercise 4(C)

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

(vii) 4.6 by 2.1

(viii) 0.568 by 6.4

Answer

(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

Multiply each number by 10, 100 and 1000:

(i) 0.5

(ii) 0.112

(iii) 4.8

(iv) 0.0359

(v) 16.27

(vi) 234.8

Answer

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.

Evaluate:

(i) 5.897 × 2.3

(ii) 0.894 × 87

(iii) 0.01 × 0.001

(iv) 0.84 × 2.2 × 4

(v) 4.75 × 0.08 × 3

(vi) 2.4 × 3.5 × 4.8

(vii) 0.8 × 1.2 × 0.25

(viii) 0.3 × 0.03 × 0.003

Answer

(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

Divide:

54.9 by 10

Answer

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

⇒ 54.9 ÷ 10 = 5.49

Hence, 54.9 ÷ 10 = 5.49

Divide:

7.8 by 100

Answer

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

⇒ 7.8 ÷ 100 = 0.078

Hence, 7.8 ÷ 100 = 0.078

Divide:

324.76 by 1000

Answer

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

⇒ 324.76 ÷ 1000 = 0.32476

Hence, 324.76 ÷ 1000 = 0.32476

Divide:

12.8 by 4

Answer

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

Divide:

27.918 by 9

Answer

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

Divide:

4.672 by 8

Answer

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

Divide:

4.32 by 1.2

Answer

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

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

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

Divide:

7.644 by 1.4

Answer

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

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

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

Divide:

4.8432 by 0.08

Answer

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

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

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

Divide each of the given numbers by 10, 100, 1000 and 10000:

2.1

Answer

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.

Divide each of the given numbers by 10, 100, 1000 and 10000:

8.64

Answer

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.

Divide each of the given numbers by 10, 100, 1000 and 10000:

5.01

Answer

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.

Divide each of the given numbers by 10, 100, 1000 and 10000:

0.0906

Answer

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.

Divide each of the given numbers by 10, 100, 1000 and 10000:

0.125

Answer

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.

Divide each of the given numbers by 10, 100, 1000 and 10000:

111.11

Answer

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.

Evaluate:

9.75 ÷ 5

Answer

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

Evaluate:

4.4064 ÷ 4

Answer

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

Evaluate:

27.69 ÷ 30

Answer

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

Evaluate:

19.25 ÷ 25

Answer

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

Evaluate:

20.64 ÷ 16

Answer

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

Evaluate:

3.204 ÷ 9

Answer

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

Evaluate:

0.125 ÷ 25

Answer

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

Evaluate:

0.14616 ÷ 72

Answer

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

Evaluate:

0.6227 ÷ 1300

Answer

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

Evaluate:

257.894 ÷ 0.169

Answer

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

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

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

Evaluate:

6.3 ÷ (0.3)²

Answer

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

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

Evaluate:

(i) 4.3 × 0.52 × 0.3

(ii) 3.2 × 2.5 × 0.7

(iii) 0.8 × 1.5 × 0.6

(iv) 0.3 × 0.3 × 0.3

(v) 1.2 × 1.2 × 0.4

(vi) 0.4 × 0.04 × 0.004

(vii) 0.5 × 0.6 × 0.7

(viii) 0.5 × 0.06 × 0.007

Answer

(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

Evaluate:

(i) (0.9)²

(ii) (0.6)² × 0.5

(iii) 0.3 × (0.5)²

(iv) (0.4)³

(v) (0.2)³ × 5

(vi) (0.2)³ × 0.05

Answer

(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

Find the cost of 36.75 kg wheat at the rate of ₹ 12.80 per kg.

Answer

Cost of wheat = Rate per kg × Weight

= ₹ 12.80 × 36.75 = ₹ 470.40

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

The cost of a pen is ₹ 56.15. Find the cost of 16 such pens.

Answer

Cost of 16 pens = Cost of one pen × 16

= ₹ 56.15 × 16 = ₹ 898.40

Hence, the cost of 16 pens is ₹ 898.40.

Evaluate:

0.0072 ÷ 0.06

Answer

Shift the decimal point of both numbers by 2 places.

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

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

Evaluate:

0.621 ÷ 0.3

Answer

Shift the decimal point of both numbers by 1 place.

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

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

Evaluate:

0.0532 ÷ 0.005

Answer

Shift the decimal point of both numbers by 3 places.

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

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

Evaluate:

0.01162 ÷ 0.14

Answer

Shift the decimal point of both numbers by 2 places.

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

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

Evaluate:

(7.5 × 40.4) ÷ 25

Answer

(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

Evaluate:

2.1 ÷ (0.1 × 0.1)

Answer

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

Hence, 2.1 ÷ (0.1 × 0.1) = 210

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

Answer

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.

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

Answer

Other number = Product ÷ One number

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

Hence, the other number is 12.8.

One dozen identical articles cost ₹ 45.96. Find the cost of each article.

Answer

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.

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

3 ÷ 8

Answer

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.

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

8 ÷ 3

Answer

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.

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

6 ÷ 5

Answer

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.

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

5 ÷ 6

Answer

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.

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

12.5 ÷ 4

Answer

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.

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

23 ÷ 0.7

Answer

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

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.

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

42 ÷ 9

Answer

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.

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

0.56 ÷ 0.11

Answer

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

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.