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Decimal to Fraction Converter

Convert any decimal number to a simplified fraction with step-by-step conversion.

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1. Enter a decimal number in the input field. 2. For repeating decimals, use the repeating notation or enter additional digits. 3. View the exact fractional representation simplified to lowest terms. 4. Review the step-by-step GCD reduction process used to simplify. 5. Click the copy button to copy the fraction result.

About This Tool

The Decimal to Fraction Converter takes any decimal number - whether terminating or repeating - and converts it into its equivalent fraction in simplest form. Enter a decimal value and the tool instantly produces the corresponding fraction, automatically reduced to lowest terms using the greatest common divisor.

This conversion is essential in many contexts. Measurements in inches often use fractions, cooking recipes call for fractional amounts, and mathematical proofs frequently require exact fractional representations rather than approximate decimals. Understanding the fractional form of a decimal also reveals its exact value without rounding errors.

The tool handles a wide range of decimal inputs, from simple cases like 0.5 (which becomes 1/2) to more complex decimals like 0.875 (which becomes 7/8). It shows the conversion steps so you can understand the process, making it a valuable learning aid alongside being a practical utility.

Formula / How It Works

For terminating decimal with n decimal places: Fraction = Decimal x 10^n / 10^n, then simplify by GCD

Frequently Asked Questions

Write the decimal over 1, then multiply both the numerator and denominator by 10 for each decimal place. For example, 0.75 = 75/100. Then simplify by dividing both by the GCD (25), giving 3/4.
Set the decimal equal to x, multiply both sides by a power of 10 to shift the repeating block, then subtract the original equation. For example, 0.333... = x, so 10x = 3.333..., then 10x - x = 3, giving 9x = 3, so x = 1/3.
Every terminating decimal and every repeating decimal can be written as a fraction. However, irrational numbers like pi (3.14159...) and the square root of 2 (1.41421...) have non-terminating, non-repeating decimals and cannot be expressed as fractions.
0.125 = 125/1000. Dividing both by the GCD (125) gives 1/8. So 0.125 as a fraction is 1/8.

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