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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