Convert any decimal value into a simplified, reduced fraction. Supports both terminating decimals and repeating (recurring) decimals.
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📋 Calculation Steps
Simplified Fraction:—
Mixed Number representation:—
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How decimals are converted back to fractions
Converting a decimal to a fraction depends on whether the decimal is terminating or repeating:
Terminating Decimals: Write the decimal as a fraction with a power of 10 in the denominator. E.g. \(0.375 = \frac{375}{1000}\). Then, find the Greatest Common Divisor (GCD) of both values (\(\text{GCD} = 125\)) and divide both to simplify: \(\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}\).
Repeating Decimals: Use algebra to eliminate the repeating part. E.g. for \(x = 0.1666...\): multiply by 100 (\(100x = 16.666...\)) and multiply by 10 (\(10x = 1.666...\)). Subtracting the two equations gives \(90x = 15\), which simplifies to \(\frac{15}{90} = \frac{1}{6}\).