Education
Decimal to Fraction Calculator
Last updated: June 19, 2026
A decimal to fraction calculator is an arithmetic utility that converts terminating or repeating decimal numbers into simplified proper fractions, improper fractions, or mixed numbers. The calculator identifies the decimal's place value, sets the digits as the numerator, and places the corresponding power of ten as the denominator. It then reduces the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor. Students, engineers, and woodworkers use this tool to translate decimal measurements into usable fractional units.
Enter a terminating decimal and the calculator returns the unsimplified fraction, the simplified fraction, the mixed-number form if the value is at least 1, and the percent equivalent.
Quick Answer
Convert decimal numbers into simplified fractions. Enter any terminating or repeating decimal to find its exact fractional and mixed number equivalent.
Use a terminating decimal like 0.75 or 1.25. · e.g. 0.75
The calculator handles terminating decimals. Repeating decimals like 0.333… need a separate method.
Step by step
- Place the decimal over the power of 10 that matches the decimal places (2): 75/100
- Divide numerator and denominator by their gcd to simplify: 3/4
Simplified fraction
3/4
0.75 as a fraction
Multiply numerator and denominator until both are whole numbers by using the matching power of 10. Then divide by their gcd.
Examples
0.75 → fraction
= 3/4 · 75%
0.125 → fraction
= 1/8 · 12.5%
1.25 → fraction
= 5/4 = 1 1/4 · 125%
How it works
A terminating decimal can always be written as a fraction whose denominator is a power of 10. The calculator counts the digits after the decimal point, builds that fraction, and then divides both numerator and denominator by their greatest common divisor to reduce it.
Form · d = digits ÷ 10^places
Simplify · n/d → (n ÷ gcd) / (d ÷ gcd)
Repeating decimals need a separate algebraic method.
Related math calculators
- Fraction to decimal calculator for the reverse conversion.
- Mixed fraction calculator
- Mixed number calculator to switch between improper fractions and mixed numbers.
- Fraction calculator for adding, subtracting, multiplying, and dividing fractions.
- Percentage calculator for the percent equivalents of any decimal or fraction.
- All education calculators.
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Frequently asked questions
Count the digits after the decimal point. Place the decimal value over the matching power of 10 (one digit goes over 10, two over 100, three over 1000, and so on). Then simplify the fraction by dividing numerator and denominator by their greatest common divisor. For 0.75 with two decimal places: 75/100 = 3/4.
Repeating decimals need a different method, usually setting up an equation: let x = 0.333…, then 10x = 3.333…, so 10x − x = 3, giving x = 3/9 = 1/3. This calculator handles terminating decimals only. If a repeating decimal is entered the result reflects whatever digits you typed (which is a finite, slightly different number).
The sign attaches to the numerator. For -0.4 the unsimplified fraction is -4/10, which simplifies to -2/5. The denominator is always positive.
When the decimal is greater than 1, the simplified fraction is improper (numerator larger than denominator). The mixed-number row shows the equivalent whole-number-plus-fraction form. For 1.25, the fraction is 5/4 and the mixed number is 1 1/4.
For terminating decimals it is exact: 0.75 returns 3/4, and 0.125 returns 1/8. JavaScript loses precision for numbers with very many decimal places (typically beyond 15 significant digits), so very long inputs can round slightly. Stick to inputs you would normally write out by hand.
Closely related. To convert a percent to a fraction, drop the percent sign and divide by 100, then convert that decimal to a fraction. For 75%, divide by 100 to get 0.75, which the calculator returns as 3/4. The percent row in the result shows the same value with a percent sign for cross-checking.
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