Fraction to decimal calculator
Convert a fraction into a decimal value with repeating-block detection when applicable.
What this calculator covers
Use this calculator to turn a fraction into a decimal while keeping the simplified form visible.
If the quotient repeats, the supplementary details call out the repeating block so you can see whether the decimal terminates or cycles.
Frequently asked questions
- How can I tell if a fraction will produce a repeating decimal?
- A fraction in lowest terms produces a terminating decimal only when the denominator's prime factors are limited to 2 and 5 — the prime factors of 10. Any other prime factor in the denominator (3, 7, 11, etc.) guarantees a repeating pattern.
- What does the repeating notation like 0.(3) mean?
- The digit or digits inside parentheses repeat infinitely. For example, 0.(3) means 0.333... and 0.(142857) means 0.142857142857..., which is the decimal for 1/7. The parentheses mark the cycle that starts repeating from that position.
- Why is the decimal value rounded to 10 places?
- The displayed decimal is truncated to 10 fraction digits for readability. Repeating decimals go on forever, so at some point a display cutoff is necessary. The repeating-block notation in the details section is the exact representation when the decimal does not terminate.
- Does the calculator simplify the fraction before converting?
- Yes. The fraction is reduced to lowest terms first, then divided. This does not change the decimal value, but it makes the repeating-block detection more straightforward and ensures the simplified form is shown alongside the decimal.
Tool
Run the calculation
Result
RESULT · DECIMAL
â„–147
Primary result
0.3333333333
1/3 simplifies to 1/3 and evaluates to 0.3333333333. The repeating cycle is 0.(3).
- Simplified fraction
- 1/3
- Decimal value
- 0.3333333333
- Repeating block
- 3
- Repeating notation
- 0.(3)
Step-by-step solution
- 1.Reduce 1/3 to lowest terms as 1/3.
- 2.Divide 1 by 3 and round the displayed decimal to 10 places, giving 0.3333333333.
- 3.Track remainders during long division to detect the repeating block 3.
Walkthrough
Visual walkthrough
Fraction-to-decimal conversion is long division with one extra check: whether a remainder repeats or disappears.
01
Reduce the fraction first
1/3
Simplifying the fraction makes the decimal behavior easier to interpret and avoids carrying extra common factors.
02
Run the division
1 / 3 = 0.3333333333
The displayed decimal is rounded to 10 fraction digits after the quotient is computed.
03
Check for repeating remainders
A zero remainder means the decimal terminates; a repeated remainder means the digit cycle repeats forever.
0.(3)