Fraction/Decimal Converter Calculator

This fraction calculator takes two fractions and performs addition, subtraction, multiplication, and division, outputting the result in lowest terms. Enter the numerator and denominator of each fraction, then press calculate to see the result. It provides accurate results through mathematical operations and is useful for education.

Fraction/Decimal Converter Calculation Method

Converting a fraction to a decimal

To convert a fraction to a decimal, divide the numerator by the denominator. For example,compute 3 ÷ 4 to get 0.75. If the division never ends and repeats, it becomes a repeating decimal. For example,compute 1 ÷ 3 to get 0.333.... You can easily convert it using a calculator or a division algorithm.

Converting a decimal to a fraction

To convert a decimal to a fraction, use a power of 10 as the denominator based on the number of decimal places. For example, 0.75can be expressed as, and reducing it to lowest terms givesbecomes. For repeating decimals, set the whole decimal as a variable, build an equation, and solve it by shifting the decimal point. For example, for 0.333..., set x=0.333..., then solve 10x−x=3 to getis obtained.

About This Calculator

Fractions and decimals are two ways of writing the same rational number, and converting between them is a routine step in cooking, carpentry, finance and engineering. Some fractions produce exact decimals; others repeat forever.

Enter a fraction to get its decimal, or enter a decimal to get the simplest equivalent fraction.

A fraction gives a terminating decimal only when its denominator has no prime factors other than 2 and 5: 3/8 is 0.375, while 1/3 is 0.333… and 1/7 repeats with a period of six digits. Any repeating decimal can be turned back into an exact fraction by aligning two shifted copies and subtracting them.

Key Formula:Fraction → decimal: a / b · Decimal → fraction: place over 10ⁿ and simplify

Frequently Asked Questions

How do I convert a fraction to a decimal?

Divide the numerator by the denominator: 3/8 = 3 ÷ 8 = 0.375. If the division never terminates, as with 1/3 = 0.333…, the decimal is called a repeating decimal.

Which fractions give terminating decimals?

Only those whose simplified denominator has no prime factors other than 2 and 5 — the prime factors of 10. So 1/8 = 0.125 terminates, while 1/3 and 1/7 repeat.

How do I convert a repeating decimal to a fraction?

Set x = 0.333… and 10x = 3.333…, then subtract to get 9x = 3, so x = 1/3. For 0.142857142857… multiply by 10⁶ and subtract: 999999x = 142857, which reduces to 1/7.

Why does 0.1 + 0.2 not equal 0.3 in code?

Binary floating point cannot represent 0.1 or 0.2 exactly, so the sum comes out as 0.30000000000000004. Compare with a tolerance, or use a decimal or rational type when working with money.

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Sources & last update

2026-10-19