Class 8 Rational Numbers as Decimals — practice questions with answers

Rational Numbers · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Write

\frac{3}{4}

as a decimal.

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Answer: A) 0.75

3 ÷ 4 = 0.75, or

\frac{3}{4} = \frac{75}{100}

= 0.75. 0.34 just writes the digits side by side.

2. What is

\frac{2}{9}

as a decimal?

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Answer: A)

0. \overline{2}

2 ÷ 9 = 0.2222…, so

\frac{2}{9} = 0. \overline{2}

3. Reena says

\frac{21}{28}

must give a recurring decimal because 28 has a factor 7. What is correct?

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Answer: A) It terminates, since

\frac{21}{28} = \frac{3}{4}

= 0.75

Reduce first:

\frac{21}{28} = \frac{3}{4}

. The denominator 4 = 2 × 2, so the decimal terminates: 0.75. The test applies only to lowest terms.

4. Express

- 0. \overline{7}

as a rational number.

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Answer: B)

- \frac{7}{9}

0. \overline{7} = \frac{7}{9}

, so

- 0. \overline{7} = - \frac{7}{9}

5. The repeating decimal

0. \overline{ab}

, where a and b are digits, equals

\frac{7}{33}

. What is the two-digit block ab?

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Answer: C) 21

\frac{7}{33} = \frac{21}{99}

, and

\frac{21}{99} = 0. \overline{21}

. So ab = 21.

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