Fraction to Decimal Calculator (Repeating Decimals)
Enter a numerator and denominator to see the exact decimal.
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Exact decimal (repeating part in brackets)
Exact decimal (repeating part in brackets)
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Type
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Fraction to Decimal Calculator (Repeating Decimals) by TheCalcTools
How the Fraction to Decimal Calculator (Repeating Decimals) works
Long division either ends (a terminating decimal) or reaches a remainder it has seen before, after which the digits repeat. The calculator tracks remainders and puts the repeating block in brackets.
A fraction in lowest terms terminates exactly when its denominator has no prime factors other than 2 and 5.
The formula
a/b terminates ⇔ b (in lowest terms) = 2^m × 5^n
Worked example
Using the default values shown in the calculator:
| Numerator | 5 |
|---|---|
| Denominator | 7 |
- 5/7 = 0.(714285).
Result:
| Exact decimal (repeating part in brackets) | 0.(714285) |
|---|---|
| Decimal value | 0.7143 |
| Percentage | 71.43% |
| Type | Repeating |
Frequently asked questions
What is 5/7 as a decimal?
0.(714285): the six digits 714285 repeat forever.
Is 0.(9) equal to 1?
Yes. 0.999… repeating is exactly 1.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.