Fraction to Decimal Converter

About Fraction to decimal converter

Converts fractions to exact decimals, and decimals back to reduced fractions, including repeating ones. It uses whole-number long division rather than floating point, so 1/3 comes out as 0.(3) instead of 0.333333 and the result is always a true answer.

How to use it

1. Pick a Direction: fraction to decimal or decimal to fraction.
2. Enter a Fraction such as 3/4, 7/2 or 1 2/3, or a Decimal such as 0.75 or 0.(3).
3. Choose a Repeating notation (parentheses like 0.(3), or a bar) and the Rounded decimal places, from 0 to 100.
4. Read the cards for Exact decimal, Simplified fraction, Mixed number, Percentage and the rounded value, and press Swap to feed the result back in.

Pi's classroom approximation

22/7

3.(142857), mixed number 3 1/7, 314.2857%, and 3.1428571429 rounded to 10 places

When to use it

• Finding the exact decimal value of a measurement such as 5/16 inch.
• Turning a repeating decimal like 0.8(3) into the fraction 5/6.
• Simplifying 18/24 to 3/4 before using it in a worksheet.
• Getting a rounded value with a chosen precision to paste into a spreadsheet or code.

Questions about Fraction to decimal converter

Why do some fractions repeat forever?

After reducing, a fraction terminates only if its denominator has no prime factors except 2 and 5. Denominators such as 3, 7 or 11 always produce a repeating cycle, like 1/7 becoming 0.(142857).

How do I enter a repeating decimal?

Put the repeating digits in parentheses, as in 1.2(45), which equals 137/110. A combining overline over the digits is also understood.

Is 0.(9) really equal to 1?

Yes, and the tool shows it: 0.(9) converts to exactly 1, which is the reduced form of 9/9.

Which inputs are rejected?

A denominator of zero, and anything that is not a whole-number fraction, mixed number, integer or decimal. The message shows the accepted forms.

Does it handle negatives?

Yes. -5/6 is shown as -0.8(3) and as the mixed number -5/6, with the sign carried on the whole value.

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