How it works
- Convert the mixed number to an improper fraction.
- Divide numerator by denominator. The whole-number quotient is the integer part of the decimal.
- If there's a remainder, append a 0 and divide again — that's the next decimal digit. Repeat.
- If the remainder eventually returns to a value seen earlier, the decimal has started repeating; mark the period with an overline.
a b/c → (a·c + b) / c → integer part + decimal expansion
FAQ
Which fractions terminate vs repeat?
A fraction in lowest terms terminates only when its denominator's prime factorisation contains only 2s and 5s (e.g. 1/8 = 0.125). Otherwise it repeats (e.g. 1/3 = 0.3).
What does the overline mean?
It marks the repeating block. So 1/7 = 0.142857 means 0.142857142857… forever.