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Calculator Answers

Decimal to Fraction Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

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.

See also: Fraction to Decimal Calculator, Percentage Calculator – 3 Ways to Calculate %, and Fraction Calculator.

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

  1. Place the decimal over the power of 10 that matches the decimal places (2): 75/100
  2. Divide numerator and denominator by their gcd to simplify: 3/4
Decimal to fraction

Simplified fraction

3/4

0.75 as a fraction

Decimal0.75
Unsimplified75/100
Simplified3/4
Percent75%

Multiply numerator and denominator until both are whole numbers by using the matching power of 10. Then divide by their gcd.

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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.

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Fraction to Decimal CalculatorConvert any fraction to a decimal and percent. Returns the simplified fraction, decimal value, percent, and mixed-number form when applicable.Percentage Calculator – 3 Ways to Calculate %Use this percent calculator to find the percentage of a number, what percent one number is of another, and the whole from a part and a percent, with step-by-step math.Fraction CalculatorAdd fractions, subtract, multiply, divide, and simplify fractions. Convert fraction to decimal and convert improper fractions to mixed numbers with step by step work.

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.