Decimal Fractions — Exercise 4(A)

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

Answer

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Convert into decimal fractions:

(i) $2\dfrac{4}{5}$

(ii) $\dfrac{79}{100}$

(iii) $\dfrac{37}{10,000}$

(iv) $\dfrac{7543}{10^4}$

(v) $\dfrac{3}{4}$

(vi) $9\dfrac{3}{5}$

(vii) $8\dfrac{5}{8}$

(viii) $5\dfrac{7}{8}$

Answer

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer

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.

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

Answer

(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

Convert the given decimals into like decimals:

(i) 0.5, 3.62, 43.981 and 232.0037

(ii) 215.78, 33.0006, 530.3 and 0.03569

Answer

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.