Express the repeating decimal 0.47 as a fraction in its lowest terms.

Express the repeating decimal $0. \overline{47}$ as a fraction in its lowest terms.

easy 1 mark Class 10 · Mathematics · Real Numbers

Answer

\frac{47}{99}

The correct answer is $\frac{47}{99}$ — The fraction $\frac{47}{99}$ is already in lowest terms because $47$ is prime and does not divide $99$ .

Let $x = 0.474747 \dots$ .
The repeating block has two digits, so multiply by $100$ : $100 x = 47.474747 \dots$ .
Subtract the original $x$ from this equation: $100 x - x = 47.474747 \dots - 0.474747 \dots$ .
This gives $99 x = 47$ .
Solve for $x$ : $x = \frac{47}{99}$ .
The fraction $\frac{47}{99}$ is already in lowest terms because $47$ is prime and does not divide $99$ .

Common mistake: Forgetting to subtract the original

x

, which leads to an incorrect numerator.

Concept tested: Conversion of repeating decimal to fraction