Fraction to Decimal Converter
Any fraction to its exact decimal, repeating digits included, plus the percent.
How to convert a fraction to a decimal
Divide the numerator by the denominator with long division. 3/8: 3.000 divided by 8 gives 0.375 and the division ends, so the decimal terminates. 1/6 gives 0.1666... and the remainder starts repeating, so the digit 6 repeats forever, written 0.1(6) or with a bar over the 6.
Which fractions terminate
A fraction in lowest terms terminates exactly when its denominator has no prime factors other than 2 and 5. Halves, quarters, eighths, fifths, tenths all terminate. Thirds, sixths, sevenths, ninths repeat: 1/7 = 0.(142857), a six-digit cycle. The repeating period is always shorter than the denominator.
Common fractions as decimals
1/2 = 0.5. 1/3 = 0.333... 1/4 = 0.25. 1/5 = 0.2. 1/6 = 0.1666... 1/8 = 0.125. 3/8 = 0.375. 2/3 = 0.666... 3/4 = 0.75. 5/8 = 0.625. 7/8 = 0.875. 1/16 = 0.0625.