Fraction to Decimal Calculator

A fraction is really an unfinished division problem. Converting it to a decimal just finishes the division — numerator divided by denominator. This calculator does that and also shows the percent form, which is the same number times 100.

The fraction to decimal formula

For a plain fraction the whole number is 0, so it reduces to numerator ÷ denominator.

Worked example

The calculator’s defaults are whole 0, numerator 3, denominator 4.

For a mixed number like 2 1/4: .

What your results mean

The decimal value is the exact result of dividing the numerator by the denominator — for fractions that terminate (like 3/4, 1/2, or 7/8) it’s a precise, finite number. For fractions like 1/3 or 5/6, the true decimal repeats forever, so the value shown is rounded to six decimal places.

The percent value is the same number scaled by 100, since “percent” literally means “per hundred.” A decimal of 0.75 and a percent of 75% describe the exact same amount, just in different units.

Common fractions and their decimals

Fractions built on 2s and 5s (halves, quarters, eighths, fifths, tenths) always terminate cleanly. Anything with a 3, 6, 7, or 9 in the simplified denominator tends to repeat.

Where this matters

Converting fractions to decimals comes up constantly in measurements, finance, and probability, where decimals are easier to compare or plug into further calculations than fractions are. If you need to go the other direction, use the decimal to fraction calculator. For the percent form on its own with more detail, see the fraction to percent calculator.

Converting by long division

When there’s no calculator around, divide the numerator by the denominator and add zeros after the decimal point as you go. For :

• 8 doesn’t go into 5, so write 0. and bring down a zero: 50.
• 8 goes into 50 six times (48), remainder 2. Bring down a zero: 20.
• 8 goes into 20 twice (16), remainder 4. Bring down a zero: 40.
• 8 goes into 40 five times exactly, remainder 0. Stop.

So . When the remainder hits zero the decimal terminates; when a remainder you’ve already seen comes back, the digits start repeating.

Predicting whether the decimal ends

You can tell before dividing. Simplify the fraction, then factor the denominator. If its only prime factors are 2 and 5, the decimal terminates, and the largest power tells you how many decimal places you’ll get. For , , so expect three places: .

If any other prime appears (3, 7, 11 and so on), the decimal repeats. , usually written . It has to repeat eventually: dividing by 11 only allows remainders 1 to 10, so one must come back.

Common mistakes

• Dividing the wrong way round. is , not . The numerator goes first.
• Truncating instead of rounding. rounds to at two places, not .
• Predicting from an unsimplified fraction. has a 3 in its denominator, but it simplifies to , which terminates.
• Losing the whole number. For , convert the fraction part to and then add the 4 back: .

A quick mental shortcut

If the denominator is a factor of 10, 100 or 1000, scale the fraction up to it and read off the decimal. , and . No division needed.

Patterns worth knowing

Some denominators produce patterns that save dividing:

• Ninths: the digit repeats. ,
• Elevenths: a two-digit block that is 9 times the numerator. , since .
• Sevenths: the same six digits rotated. and

Rounding repeating decimals

Round at the place you need, looking only at the next digit. rounds to 0.83 at two places, and rounds to 0.67. For money, two places is standard; for measurements, match the precision of the tool.

Try these

For more, the decimal practice problems generate fresh sets each time.