Fraction to Decimal Calculator
From 3/8 to 0.375 in one step.
Fraction to Decimal Calculator
Convert a fraction to a decimal and percentage, and reduce it to lowest terms.
Between 0 and 12. Repeating decimals are rounded at this point.
The numerator and denominator must be whole numbers. A negative denominator is normalised by moving the sign to the numerator.
Decimal
0.375
Terminating decimal
- Percentage
- 37.5%
- Simplified fraction
- 3 / 8
- Mixed number
- �
A fraction terminates only when its simplified denominator is built from 2s and 5s. Otherwise the decimal repeats forever.
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What This Calculator Does
The Fraction to Decimal Calculator converts any fraction into a decimal and a percentage, and reduces it to lowest terms. It also reports the mixed-number form when the numerator is larger than the denominator.
How It Works
A fraction is a division: the numerator divided by the denominator. The decimal is that quotient; multiply by 100 for the percentage. To simplify, divide both parts by their greatest common divisor. A fraction is terminating when the reduced denominator has only 2 and 5 as prime factors, and repeating otherwise.
Example
For 6/8, dividing gives 0.75, which is 75%. The greatest common divisor of 6 and 8 is 2, so the fraction simplifies to 3/4. For 1/3 the decimal is 0.333…, a repeating decimal with no exact finite form.
Formula
Decimal = numerator / denominatorPercent = (numerator / denominator) × 100Divide numerator and denominator by gcd(n, d)Reading the Results
Decimal
The exact quotient when it terminates, or a rounded value when it repeats. The simplified fraction is shown beside it so the exact value is never lost.
Simplified fraction
The same value with the numerator and denominator divided by their greatest common divisor.
Mixed number
The whole-number part and the remaining proper fraction, useful for measurements such as 2 3/4 inches.
Sources and References
NIST Digital Library of Mathematical Functions
Rational numbers and repeating decimals
A reduced fraction has a terminating decimal exactly when its denominator is of the form 2ᵃ5ᵇ.
References identify the method or data behind this calculator. Where a standard or tariff changes, the current edition applies, and the assumptions stated above take precedence over a remembered figure.
Frequently Asked Questions
How do I convert a fraction to a decimal by hand?
Divide the numerator by the denominator. For 3/8, 8 goes into 3.000 three times (0.3), leaving 0.6, then 7 times (0.07), leaving 0.04, then 5 times (0.005) — giving 0.375.
Which fractions produce repeating decimals?
Any fraction whose simplified denominator has a prime factor other than 2 or 5. So 1/3, 1/6, and 5/7 repeat, while 1/8, 3/20, and 7/25 terminate.
Can the denominator be negative?
Mathematically yes, but the usual convention moves the sign to the numerator. This calculator normalises the sign, so 3/−8 is treated as −3/8 and reported as −0.375.
Why simplify a fraction if the decimal is the same?
Simplified fractions are easier to compare, add, and use in recipes or measurements. 3/4 is immediately readable; 24/32 is not.