Express 0.6 in the form p/q, where p and q are integers and q ≠ 0.

Express $0. \overline{6}$ in the form $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \neq = 0$ .

easy MCQ 1 mark Class 9 · Mathematics · Number Systems

Answer

\frac{2}{3}

The correct answer is $\frac{2}{3}$ — Solve for $x$ : $x = \frac{6}{9} = \frac{2}{3}$ .

Let $x = 0. \overline{6} = 0.6666...$ (Equation 1).
Multiply both sides of Equation 1 by $10$ , since one digit is repeating: $10 x = 6.6666...$ (Equation 2).
Subtract Equation 1 from Equation 2: $10 x - x = (6.6666...) - (0.6666...)$ , which simplifies to $9 x = 6$ .
Solve for $x$ : $x = \frac{6}{9} = \frac{2}{3}$ .

Common mistake: Writing

0. \overline{6}

\frac{6}{10}

by treating it as a terminating decimal instead of a recurring one.

Concept tested: Expressing non-terminating recurring decimals as rational numbers