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Fraction to Decimal Calculator

Convert any fraction or mixed number to a decimal. Shows if it terminates or repeats, plus long division steps.

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What is Fraction to Decimal Calculator?

A fraction to decimal calculator converts any fraction (proper, improper, or mixed number) to its decimal equivalent. It also tells you whether the decimal terminates (ends) or repeats, shows the repeating block using bar notation, and displays the first 10 steps of long division so you can see exactly how the conversion works.

How to use

  1. 1 Enter the numerator and denominator in the Simple Fraction fields.
  2. 2 Or switch to Mixed Number mode and enter a whole number, numerator, and denominator.
  3. 3 The decimal result, percentage, and terminating/repeating status appear instantly.
  4. 4 Scroll down to see the long division steps table.

Formula

Decimal = numerator ÷ denominator. A fraction a/b terminates if and only if, after simplification, b has no prime factors other than 2 and 5. Otherwise the decimal repeats with a period of at most b−1 digits.

Example calculation

3/4 = 0.75 (terminates — denominator 4 = 2²). 1/3 = 0.333… (repeats — denominator 3 has factor 3). 1/7 = 0.142857142857… (period 6). 2 1/4 = 9/4 = 2.25 (terminates).

Frequently asked questions

How do you convert a fraction to a decimal?

Divide the numerator by the denominator using long division. The quotient is the decimal. For example, 3 ÷ 4 = 0.75.

How do you know if a fraction is a repeating decimal?

After simplifying the fraction, check the denominator's prime factors. If it only contains 2s and 5s, the decimal terminates. Any other prime factor (3, 7, 11, …) causes the decimal to repeat.

What is a repeating decimal?

A repeating decimal has a digit or group of digits that repeats infinitely, such as 0.333… (the 3 repeats) or 0.142857142857… (the block 142857 repeats). The repeating part is often written with a bar over it.

What is a mixed number?

A mixed number is a whole number plus a proper fraction — for example, 2 3/4. To convert it to an improper fraction: multiply the whole number by the denominator and add the numerator: (2×4)+3 = 11, so 2 3/4 = 11/4.

How many decimal places does a repeating decimal have?

The repeating block length (period) is at most denominator − 1. For 1/7 the period is 6 (142857); for 1/3 the period is 1 (3).