Decimal to Fraction Converter

Convert any terminating or repeating decimal number into an exact simplified fraction and mixed number with step-by-step reduction steps.

Decimal Input

Live conversion
Common Decimals:

Fractions eliminate floating-point rounding errors and provide exact mathematical answers for construction and engineering.

Simplified Fraction
3/4
Mixed Number—
Decimal: 0.75GCD Divisor: 25
Numerator3
Denominator4
Percentage75.00%
Raw Ratio75/100

Step-by-Step Reduction

1. Write as ratio: 75 / 100

2. Calculate GCD: GCD(75, 100) = 25

3. Divide by GCD: (75 ÷ 25) / (100 ÷ 25) = 3/4

How Decimal to Fraction Conversion Works

Converting a terminating decimal to a fraction is achieved by placing the digits over a power of 10 equal to the number of decimal places, followed by dividing the numerator and denominator by their Greatest Common Divisor (GCD).

1. Terminating Decimal Conversion Formula
Fraction=
Decimal × 10ᵏ ÷ GCD10ᵏ ÷ GCD
Step-by-Step Calculation Breakdown (Example: 0.75)
Step 1: Express over Power of 10 (2 decimal places = 10² = 100)
• 0.75 = 75 / 100
Step 2: Find Greatest Common Divisor GCD(75, 100)
• GCD(75, 100) = 25
Step 3: Divide Both by GCD for Irreducible Form
• 75 ÷ 25 = 3 and 100 ÷ 25 = 4
• Simplified Fraction = 3/4

Common Decimal to Fraction Conversion Chart

DecimalFractionPercentageCommon Context
0.51/250%Half
0.251/425%Quarter
0.753/475%Three Quarters
0.1251/812.5%Eighth inch
0.3753/837.5%Three eighths
0.6255/862.5%Five eighths
0.8757/887.5%Seven eighths
0.06251/166.25%Sixteenth inch

Frequently Asked Questions

How do you convert a decimal into a fraction?
Count the number of decimal places after the point (say k). Place the decimal digits over 10^k to form an initial fraction. Then compute the greatest common divisor (GCD) of the numerator and denominator and divide both by this GCD to obtain the simplest irreducible fraction.
How do you convert a repeating decimal into a fraction?
For a repeating decimal like 0.333..., set x = 0.333... Multiply by 10 (10x = 3.333...), subtract x (10x − x = 3), yielding 9x = 3, so x = 3/9 = 1/3.
What is an improper fraction vs a mixed number?
An improper fraction has a numerator greater than or equal to its denominator (e.g. 21/8). A mixed number expresses this as a whole integer plus a proper fraction (e.g. 2 5/8). Both describe the exact same quantity.
Why convert decimals to fractions?
Fractions provide infinite exact precision without rounding error. They are standard in woodworking, imperial measurements (inches), culinary recipes, and formal algebraic proofs.

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