# Worksheet on Rational Number as Decimal Numbers

Practice the questions given in the worksheet on rational number as decimal numbers.

A fraction $$\frac{a}{b}$$ (in its lowest terms) is a terminating decimal only when its denominator that is b can be expressed as n = 2^m5^n where m, n = 0, 1, 2, ....

A fraction $$\frac{a}{b}$$ (in its lowest terms) is a recurring decimal only when its denominator that is b has a prime factor other than 2 or 5.

1. Which of the following will changes into a terminating decimal? Justify.

$$\frac{13}{125}$$, $$\frac{2}{9}$$, $$\frac{23}{60}$$, $$\frac{7}{250}$$

2. Write the following fractions as decimal number:

(i) $$\frac{1}{4}$$

(ii) $$\frac{17}{40}$$

(iii) $$\frac{11}{9}$$

(iv) $$\frac{13}{44}$$

(v) $$\frac{4}{7}$$

3. Which of the following will be converted into a nonterminating decimal? Justify.

$$\frac{3}{5}$$, -$$\frac{9}{75}$$, $$\frac{7}{20}$$, $$\frac{4}{30}$$

4. Express $$\frac{5}{48}$$ as a decimal fraction correct to four decimal places.

5. Which of the following will change into a recurring decimal? Justify.

$$\frac{3}{4}$$, $$\frac{7}{150}$$, -$$\frac{11}{200}$$, $$\frac{5}{44}$$

6. Without actual division, find which of the following fractions are terminating decimals:

(i) $$\frac{7}{16}$$

(ii) $$\frac{21}{80}$$

(iii) $$\frac{136}{250}$$

(iv) $$\frac{5}{6}$$

(v) $$\frac{54}{60}$$

(vi) $$\frac{48}{55}$$

(iii) $$\frac{44}{63}$$

(iv) $$\frac{115}{640}$$

7. If $$\frac{3}{14}$$ is changed into a decimal number, what type of a decimal number will it be?

Answers for the worksheet on rational number as decimal numbers are given below.

1. $$\frac{13}{125}$$, $$\frac{7}{250}$$

2. (i) 0.25

(ii) 0.425

(iii) 2.$$\dot{2}$$

(iv) 0.29$$\dot{5}$$$$\dot{4}$$

(v) 0.$$\bar{538461}$$

3. -$$\frac{9}{75}$$, $$\frac{4}{30}$$

4. 0.1042

5. $$\frac{7}{150}$$, $$\frac{5}{44}$$

6. (i) $$\frac{7}{16}$$

(ii) $$\frac{21}{80}$$

(iii) $$\frac{136}{250}$$

(v) $$\frac{54}{60}$$

(iv) $$\frac{115}{640}$$

7. Nonterminating, recurring

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