Mixed number to decimal

Convert any mixed number to a decimal. Choose how many decimal places to show; repeating decimals are detected and the period marked with an overline.

Mixed number input

Decimal value
2.3
Improper fraction
7/3
Rounded to dp
2.3333333333
Repeats?
Yes — period 1

How it works

  1. Convert the mixed number to an improper fraction.
  2. Divide numerator by denominator. The whole-number quotient is the integer part of the decimal.
  3. If there's a remainder, append a 0 and divide again — that's the next decimal digit. Repeat.
  4. 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.

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