About the Fraction to Decimal Converter
This tool divides the numerator by the denominator to give a fraction's decimal value, so 3/4 becomes 0.75 and 1/3 becomes 0.3333333333. Convert several at once, one fraction per line. It is handy for schoolwork, for converting a ratio to a decimal, and for feeding a fraction into a calculation that needs a decimal.
To go the other way and express a decimal as a fraction in lowest terms, use Decimal to Fraction.
Whether the result stops or runs on forever is decided entirely by the denominator once the fraction is in lowest terms. If its only prime factors are 2 and 5, the factors of ten, the decimal terminates: 1/8 is 0.125 and 7/40 is 0.175. Any other prime factor makes it repeat, and the repeating block is never longer than one less than the denominator, which is why 1/7 cycles through 142857 and 1/3 gives an endless run of threes.
Repeating values are shown as digits to the limit of double precision rather than with the overline or bracket notation used in textbooks, so read 0.3333333333 as 1/3 rounded and not as an exact value. That is fine for a measurement and wrong for money, where a third of a penny has to be rounded somewhere deliberately. Improper fractions such as 7/4 work and give 1.75, while a zero denominator is undefined and reported. To express the same ratio as a percentage, the Percentage Calculator handles the multiplication.
How to use
- Paste fractions like 3/4, one per line.
- Copy the decimal values.
- Swap to convert decimals back to fractions.
Common questions
- How are repeating decimals shown?
- To the precision of a double-precision number, so 1/3 shows many 3s rather than a bar notation.
- Can I convert mixed numbers?
- Convert the fractional part and add the whole number, or enter an improper fraction such as 7/4.
- What if the denominator is zero?
- Division by zero is undefined and reported as an error.