Fraction to Decimal Calculator

How to convert a fraction to a decimal

A fraction is a division written in a different way. The bar between the numerator (top) and the denominator (bottom) means "divided by", so converting to a decimal is just carrying out that division.

decimal = numerator ÷ denominator

1. Type the numerator, the number above the bar, into the first box.
2. Type the denominator, the number below the bar, into the second box. It cannot be zero, because division by zero has no value.
3. Press the button. The decimal appears in the Decimal row.

Both boxes accept decimals and negative numbers, so 2.5/4 and −5/8 work too. The result is rounded to four decimal places. A whole-number answer is shown without a decimal point (7/7 gives 1), and an answer that needs only one or two decimals is written with two (1/2 gives 0.50, 3/4 gives 0.75).

Worked examples

A terminating decimal: 7/16. Long division gives 70 ÷ 16 = 4 remainder 6, then 60 ÷ 16 = 3 remainder 12, then 120 ÷ 16 = 7 remainder 8, then 80 ÷ 16 = 5 remainder 0. The remainder reaches zero, so the digits 4, 3, 7, 5 are the whole answer: 7/16 = 0.4375.

A repeating decimal: 5/6. Dividing 5 by 6 gives 0.8333… with the digit 3 repeating forever. The calculator rounds it to four places and shows 0.8333. Rounding a repeating decimal always leaves a tiny error, so keep the fraction itself when you need an exact value.

A mixed number: 3 2/5. First turn it into an improper fraction: 3 × 5 + 2 = 17, so 3 2/5 = 17/5. Then 17 ÷ 5 = 3.4, which the calculator shows as 3.40. The whole part stays in front of the decimal point and the fraction part supplies the digits after it.

A negative fraction: −9/4. The sign carries straight through: 9 ÷ 4 = 2.25, so −9/4 = −2.25. Entering the minus sign in either the numerator or the denominator gives the same answer.

An improper fraction: 22/7. Because the numerator is larger than the denominator the result is above 1: 22 ÷ 7 = 3.142857…, shown as 3.1429. This is a well-known approximation of π.

Terminating or repeating?

Every fraction turns into a decimal that either stops (a terminating decimal) or repeats a block of digits forever (a repeating decimal). You can tell which before dividing. First reduce the fraction to lowest terms, then factor the denominator:

• If the only prime factors of the denominator are 2 and 5, the decimal terminates. Examples: 3/8 (8 = 2³) gives 0.375 and 7/20 (20 = 2² × 5) gives 0.35.
• If the denominator has any other prime factor, such as 3 or 7, the decimal repeats. Examples: 1/12 (12 = 2² × 3) gives 0.08333… and 1/7 gives 0.142857142857…, where the block 142857 repeats.

The reason is that our number system works in tens, and 10 = 2 × 5. A fraction can only be written with a finite number of decimal digits if its denominator divides some power of 10, which means its denominator can contain no primes other than 2 and 5. To simplify a fraction before checking, use the simplify fractions calculator.

Fraction to decimal conversion table

Common mistakes

• Dividing the wrong way round. The numerator is divided by the denominator, never the reverse. 1/4 is 0.25, not 4.
• Rounding too early. If you round 1/3 to 0.33 and then multiply by 3 you get 0.99, not 1. Keep extra digits until the last step.
• Reading the display as exact. A result such as 0.3333 is a rounded value of a decimal that never ends.
• Splitting a mixed number wrongly. 2 1/4 is 2 + 0.25 = 2.25, not 2.14. Convert only the fraction part, or turn the whole thing into an improper fraction first.

Going the other way and related conversions

• Turn a decimal back into a fraction with the decimal to fraction calculator.
• Express a fraction as a percentage with the fraction to percent calculator.
• Add, subtract, multiply and divide fractions in the fraction calculator.
• The fraction to decimal converter does the same job in converter form.