Express the repeating decimal 0.123 as a fraction in lowest terms.

Express the repeating decimal $0. \overline{123}$ as a fraction in lowest terms.

medium 2 marks Class 10 · Mathematics · Real Numbers

Answer

\frac{41}{333}

The correct answer is $\frac{41}{333}$ — Simplify the fraction by dividing numerator and denominator by their HCF $3$ : $\frac{123 \div 3}{999 \div 3} = \frac{41}{333}$ , which is already in lowest terms.

Step-by-step solution

Let $x = 0. \overline{123}$ .
The repeating block has three digits, so multiply by $1 0^{3} = 1000$ : $1000 x = 123. \overline{123}$ .
Subtract the original equation: $1000 x - x = 123. \overline{123} - 0. \overline{123}$ .
This gives $999 x = 123$ .
Solve for $x$ : $x = \frac{123}{999}$ .
Simplify the fraction by dividing numerator and denominator by their HCF $3$ : $\frac{123 \div 3}{999 \div 3} = \frac{41}{333}$ , which is already in lowest terms.

Common mistake: Using

1 0^{2}

instead of

1 0^{3}

because the block has three digits

Concept tested: Converting repeating decimals to fractions

Published 22 August 2026 · How this solution was prepared and checked

Express the repeating decimal 0.123 as a fraction in lowest terms.

Step-by-step solution

Related questions

Express the repeating decimal $0. \overline{123}$ as a fraction in lowest terms.