Decimal Fractions — Exercise 5(A)

Write each of the following decimals in figures:

(i) Seventy three point eight four.

(ii) Three hundred forty six point zero nine five.

(iii) Five hundred eight point two six.

(iv) Nineteen point six one eight.

(v) Zero point seven nine three.

(vi) Ten point zero zero seven.

Answer

(i) 73.84

(ii) 346.095

(iii) 508.26

(iv) 19.618

(v) 0.793

(vi) 10.007

Write the place value of each digit in each of the following decimals:

(i) 46.38

(ii) 57.095

(iii) 132.405

(iv) 19.006

Answer

(i) We can arrange the digits of 46.38 in the place value chart, as shown below:

The place value of each digit is given below:

(ii) We can arrange the digits of 57.095 in the place value chart, as shown below:

The place value of each digit is given below:

(iii) We can arrange the digits of 132.405 in the place value chart, as shown below:

The place value of each digit is given below:

(iv) We can arrange the digits of 19.006 in the place value chart, as shown below:

The place value of each digit is given below:

Write each of the following decimals in expanded form:

(i) 53.48

(ii) 6.927

(iii) 10.084

(iv) 8.005

(v) 274.503

(vi) 31.02

(vii) 1635.72

Answer

(i) We have,

$53.48 = 5 \times 10 + 3 \times 1 + 4 \times \dfrac{1}{10} + 8 \times \dfrac{1}{100} \\[1em] = 50 + 3 + \dfrac{4}{10} + \dfrac{8}{100}$

(ii) We have,

$6.927 = 6 \times 1 + 9 \times \dfrac{1}{10} + 2 \times \dfrac{1}{100} + 7 \times \dfrac{1}{1000} \\[1em] = 6 + \dfrac{9}{10} + \dfrac{2}{100} + \dfrac{7}{1000}$

(iii) We have,

$10.084 = 1 \times 10 + 0 \times 1 + 0 \times \dfrac{1}{10} + 8 \times \dfrac{1}{100} + 4 \times \dfrac{1}{1000} \\[1em] = 10 + \dfrac{8}{100} + \dfrac{4}{1000}$

(iv) We have,

$8.005 = 8 \times 1 + 0 \times \dfrac{1}{10} + 0 \times \dfrac{1}{100} + 5 \times \dfrac{1}{1000} \\[1em] = 8 + \dfrac{5}{1000}$

(v) We have,

$274.503 = 2 \times 100 + 7 \times 10 + 4 \times 1 + 5 \times \dfrac{1}{10} + 0 \times \dfrac{1}{100} + 3 \times \dfrac{1}{1000} \\[1em] = 200 + 70 + 4 + \dfrac{5}{10} + \dfrac{3}{1000}$

(vi) We have,

$31.02 = 3 \times 10 + 1 \times 1 + 0 \times \dfrac{1}{10} + 2 \times \dfrac{1}{100} \\[1em] = 30 + 1 + \dfrac{2}{100}$

(vii) We have,

$1635.72 = 1 \times 1000 + 6 \times 100 + 3 \times 10 + 5 \times 1 + 7 \times \dfrac{1}{10} + 2 \times \dfrac{1}{100} \\[1em] = 1000 + 600 + 30 + 5 + \dfrac{7}{10} + \dfrac{2}{100}$

Write each of the following as a decimal number:

(i) 60 + 8 + $\dfrac{4}{10} + \dfrac{5}{100}$

(ii) 500 + 4 + $\dfrac{6}{10} + \dfrac{8}{100} + \dfrac{3}{1000}$

(iii) 300 + 20 + $\dfrac{1}{10} + \dfrac{6}{1000}$

(iv) 2000 + 80 + $\dfrac{4}{100} + \dfrac{8}{1000}$

(v) 6000 + 3 + $\dfrac{2}{10} + \dfrac{7}{1000}$

Answer

(i) We have,

$60 + 8 + \dfrac{4}{10} + \dfrac{5}{100} \\[1em] = 6 \times 10 + 8 \times 1 + 4 \times \dfrac{1}{10} + 5 \times \dfrac{1}{100} \\[1em] = 68.45$

(ii) We have,

$500 + 4 + \dfrac{6}{10} + \dfrac{8}{100} + \dfrac{3}{1000} \\[1em] = 5 \times 100 + 0 \times 10 + 4 \times 1 + 6 \times \dfrac{1}{10} + 8 \times \dfrac{1}{100} + 3 \times \dfrac{1}{1000} \\[1em] = 504.683$

(iii) We have,

$300 + 20 + \dfrac{1}{10} + \dfrac{6}{1000} \\[1em] = 3 \times 100 + 2 \times 10 + 0 \times 1 + 1 \times \dfrac{1}{10} + 0 \times \dfrac{1}{100} + 6 \times \dfrac{1}{1000} \\[1em] = 320.106$

(iv) We have,

$2000 + 80 + \dfrac{4}{100} + \dfrac{8}{1000} \\[1em] = 2 \times 1000 + 0 \times 100 + 8 \times 10 + 0 \times 1 + 0 \times \dfrac{1}{10} + 4 \times \dfrac{1}{100} + 8 \times \dfrac{1}{1000} \\[1em] = 2080.048$

(v) We have,

$6000 + 3 + \dfrac{2}{10} + \dfrac{7}{1000} \\[1em] = 6 \times 1000 + 0 \times 100 + 0 \times 10 + 3 \times 1 + 2 \times \dfrac{1}{10} + 0 \times \dfrac{1}{100} + 7 \times \dfrac{1}{1000} \\[1em] = 6003.207$

Write each of the following numerals as decimals:

(i) $2\dfrac{7}{10}$

(ii) $43\dfrac{3}{10}$

(iii) $6\dfrac{15}{100}$

(iv) $18\dfrac{9}{100}$

(v) $5\dfrac{123}{1000}$

(vi) $4\dfrac{37}{1000}$

(vii) $10\dfrac{8}{1000}$

Answer

(i) We have,

$2\dfrac{7}{10}=2+\dfrac{7}{10}=2+0.7=2.7$

Hence, the decimal form is 2.7.

(ii) We have,

$43\dfrac{3}{10}=43+\dfrac{3}{10}=43+0.3=43.3$

Hence, the decimal form is 43.3.

(iii) We have,

$6\dfrac{15}{100}=6+\dfrac{15}{100}=6+0.15=6.15$

Hence, the decimal form is 6.15.

(iv) We have,

$18\dfrac{9}{100}=18+\dfrac{9}{100}=18+0.09=18.09$

Hence, the decimal form is 18.09.

(v) We have,

$5\dfrac{123}{1000}=5+\dfrac{123}{1000}=5+0.123=5.123$

Hence, the decimal form is 5.123.

(vi) We have,

$4\dfrac{37}{1000}=4+\dfrac{37}{1000}=4+0.037=4.037$

Hence, the decimal form is 4.037.

(vii) We have,

$10\dfrac{8}{1000}=10+\dfrac{8}{1000}=10+0.008=10.008$

Hence, the decimal form is 10.008.