three eighths
- Numerator
- 3
- Denominator
- 8
- Decimal places to show
- 8
As a decimal0.38
Eight is two cubed, so it terminates
Open this exampleMath & Statisticsfractions
Fraction to Decimal Calculator
A fraction as a decimal and a percentage, with whether the decimal terminates. Once reduced, only denominators built from twos and fives terminate in base ten.
Also called: fraction to decimal, convert fraction.
As a decimal
0.38
3/8 is 0.38, or 37.5%. The decimal terminates, because the reduced denominator is built only from twos and fives.
As a percentage
37.5%
Simplified fraction
3/8
Does it terminate
The decimal terminates, because the reduced denominator is built only from twos and fives.
The reciprocal
2.67
Method and background
How this is calculated
Dividing gives the decimal. Whether it ends is decided entirely by the reduced denominator: because we write in base ten, which factors into two and five, a denominator whose only prime factors are those two divides cleanly. Any other prime factor leaves a remainder cycle that repeats forever, which is why a third is 0.333 and an eighth is exactly 0.125.
a fraction is a division- n
- Numerator
- m
- Denominator
Worked examples
Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.
a third repeats
- Numerator
- 1
- Denominator
- 3
- Decimal places to show
- 8
As a decimal0.33
boundary: three shares no factor with ten
Open this exampleMethod and limits
What it assumes
- Base ten.
What it deliberately does not model
- The repeating block itself is not printed, only whether one exists.
Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator
Frequently asked questions
- Why does 1/3 repeat but 1/8 does not?
- Eight is two cubed and ten is two times five, so eight divides cleanly into a power of ten. Three shares no factor with ten, so the division never resolves.