Convert fractions to exact decimal expansions and decimals back to simplified fractions, including repeating notation such as 0.1(6). See the mixed number, percentage, reciprocal, and a practical nearby fraction without losing the exact relationship.
Step by step
01Choose a direction
Start with a numerator and denominator, or paste a terminating or repeating decimal.
02Enter the value
Repeating digits can be written in parentheses, as in 0.1(6), or with an ellipsis.
03Read the exact form
Fractions are reduced with the sign kept in the numerator; decimals show the non-repeating prefix and repeating cycle.
04Use the related forms
Copy the mixed number, percentage, reciprocal, rounded value, or closest useful fraction.
Worked example
Given
Exact decimal expansion
1 ÷ 6 = 0.1666…
fixed prefix = 1
repeating cycle = 6
notation = 0.1(6)Writing 0.1667 is convenient but approximate. The repeating form preserves the exact value and converts back to 1/6.
Why this one
Every rational number terminates or repeats
A fraction of integers cannot produce an irregular infinite decimal: after a finite prefix, its remainders either reach zero or repeat.
Only factors 2 and 5 terminate in base ten
After simplification, a denominator made only from 2s and 5s gives a terminating decimal. Any other prime factor creates a repeating cycle.
Simplifying preserves value
Dividing numerator and denominator by their GCD changes the notation, not the number.
Approximations need a denominator limit
Values such as π are not rational. A nearby fraction is a deliberate approximation whose usefulness depends on how large a denominator you will accept.
The judgement call
Exact ratio for algebra or code
Fraction
It preserves the value without rounding.
Money or a measured display
Rounded decimal
A fixed number of places matches the required precision.
A repeating decimal in homework
Cycle notation
Parentheses identify exactly which digits recur.
A quantity larger than one
Mixed number
It is easier to read while the improper fraction remains best for calculation.
Reference
FAQ
Divide the numerator by the denominator. The tool performs long division so it can identify an exact repeating cycle instead of merely rounding the result.
Put the recurring digits in parentheses: 0.(3) means 0.333…, and 0.1(6) means 0.1666….
A typed terminating decimal is treated exactly. More decimal places create a larger power-of-ten denominator before common factors are cancelled.
The closest simple fraction is a continued-fraction approximation with a bounded denominator, useful for irrational values or long measured decimals but distinct from an exact conversion.
No. Division by zero is undefined, so a fraction with denominator zero cannot be converted.
Conversions use local integer and decimal arithmetic in your browser. Your values are never uploaded.
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