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Fraction to Decimal Calculator

Enter a fraction to see it as a decimal. Repeating digits are marked in brackets, and you can round to anything from a whole number to ten places.

Your fraction

Type a fraction (5/8), an improper fraction (41/10) or a mixed number (2 3/4).
The exact value keeps every digit, and marks a repeating block in brackets.
Long division
5 ÷ 8 = 0.625
Rounding
None — every digit shown
5/8 as a decimal
0.625
Fraction in lowest terms
5/8
Exact value
0.625
Decimal type
Terminating decimal
As a percentage
62.5%

How to use this calculator

  1. Type the fraction as 5/8. Improper fractions like 41/10 and mixed numbers like 2 3/4 both work.
  2. Leave the rounding on Exact value to see every digit, or choose the number of decimal places you need.
  3. Read the decimal above the supporting figures. The long-division line under the inputs shows the division being performed.

Rounding changes what is displayed as the headline, never what the fraction is. The exact value stays on screen beside it, so a figure rounded to two places can still be checked against the true one.

How a fraction becomes a decimal

A fraction is already a division: the line means "divided by". So converting one is simply carrying that division out.

Decimal = Numerator ÷ Denominator
  • Numerator — the top number, e.g. 5
  • Denominator — the bottom number, e.g. 8
  • Decimal — the answer, e.g. 0.625

There is a shortcut when the denominator divides into a power of ten. Scale the fraction until the bottom is 10, 100 or 1,000, and the top is the answer: 2/5 = 4/10 = 0.4 and1/25 = 4/100 = 0.04. Long division is the general method for when it does not.

Long division also explains repeating decimals. Each step leaves a remainder, and there are only so many remainders a denominator can produce — dividing by 7 can only ever leave 1 through 6. Once a remainder comes back, the digits that followed it come back too, for ever. That is why 1/7 repeats after exactly six digits.

Common fractions as decimals

Terminating and repeating decimals compared
FractionDecimalType
1/40.25Terminating
5/80.625Terminating
1/250.04Terminating
1/30.(3)Repeating, 1 digit
1/60.1(6)Repeating, 1 digit
1/70.(142857)Repeating, 6 digits

The split down the Type column is decided entirely by the denominator. Four, eight and twenty-five are built from 2s and 5s, so they terminate; three, six and seven are not, so they repeat.

Frequently asked questions

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. For 5/8 that is 5 ÷ 8 = 0.625. Long division is the reliable method by hand, and it is what the calculator does — digit by digit, tracking the remainder.

What do the brackets in the answer mean?

They mark the digits that repeat for ever. 0.(3) means 0.3333… and 0.1(6) means 0.16666…. Written by hand the same thing is shown with a line over the repeating digits, which cannot be typed, so brackets are used instead.

Which fractions give a terminating decimal?

Only those whose denominator, in lowest terms, has no prime factors other than 2 and 5. So halves, quarters, fifths, eighths, tenths and twentieths all terminate, while thirds, sevenths, ninths and elevenths repeat. That is a fact about base ten, not about the fraction.

How many decimal places should I use?

Enough for the job, and no more. Set the rounding to two places for money, three for most measurements, or leave it on the exact value when you need to know precisely what the fraction is. The exact value is always shown alongside, so rounding never hides the real figure.

Can I enter an improper fraction or a mixed number?

Yes. 41/10 gives 4.1, and typing it as 4 1/10 gives the same answer. The stat row shows the fraction in lowest terms with its mixed-number form, so you can check the conversion went the way you meant.

Is 0.999… really equal to 1?

Yes. It is not a number just below 1 — it is 1, written differently. Any fraction whose decimal repeats nines is the same as the terminating decimal one step above it, which is worth knowing before assuming a calculator has rounded something.