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.

Answers:

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

9th Grade Math

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