When $ 0.292929...... $ is converted into a fraction, then the... | Mathematics MCQ

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MathematicsPrevious Year Paper 2024

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When $0.292929......$ is converted into a fraction, then the result is:

$\frac{1}{5}$

$\frac{29}{99}$

$\frac{2}{9}$

$\frac{29}{100}$

Correct Answer

📐 MA • Math Recurring Decimal to FractionMathematicsPrevious Year Paper 2024

Option B

$\frac{29}{99}$

Quick Summary:

Converting Pure Recurring Decimal 0.292929... to a Fraction

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📐MAMath SolutionRecurring Decimal to Fraction⏱️ 15 Seconds

📋 Given

Decimal: $0.292929... = 0.\overline{29}$

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Algebraic Conversion

Let $x = 0.\overline{29} = 0.292929...$ Multiplying both sides by $100$ (since 2 digits repeat): $100x = 29.292929...$

100x=29.29‾100x = 29.\overline{29}100x=29.29

Subtract to Eliminate Repeating Period

$100x - x = 29.2929... - 0.2929...99x = 29 \implies x = \frac{29}{99}$

x=2999x = \frac{29}{99}x=9929​

✅

Option B is correct — 29/99

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