A mixed number is the sum of a whole number and a proper fraction written side by side: 3 7/10 means 3 + 7/10. OpenStax notes that when the number to the left of a decimal point is zero the decimal converts to a proper fraction, and when it is not zero the result is a mixed number.
Formula
whole n/d = (whole × d + n) / d
- whole: the whole-number part.
- n / d: the numerator and denominator of the fractional part.
Example
4.09 = 4 9/100. As an improper fraction: (4 × 100 + 9)/100 = 409/100. Likewise 3.7 = 3 7/10 = (3 × 10 + 7)/10 = 37/10. The fractional part is simplified with the greatest common factor; for 2.5 = 2 5/10, dividing by 5 gives 2 1/2.
The decimal to fraction guide shows the full routine, and the decimal to fraction calculator returns both forms.
Common mistakes
- Dropping the whole part when converting, which turns 4.09 into 9/100.
- Adding instead of multiplying when converting to an improper fraction.