How do I convert a fraction into a decimal and percentage?
A fraction is a division statement: the numerator is divided by the denominator. Multiplying the resulting decimal by 100 expresses the same value as a percentage.
Reading a fraction as division
The numerator is divided by the denominator to produce a decimal. Multiplying that decimal by 100 gives the percentage.
The reciprocal swaps denominator and numerator, while remainder reports what is left after integer division. A zero denominator cannot produce a finite decimal or percentage.
Numerator divided by denominator
Decimal = Numerator ÷ DenominatorPercentage = Decimal × 100One value in fraction, decimal and percent form
The default numerator and denominator are converted into decimal and percentage forms without changing their underlying proportion.
Exact fractions and rounded repeating decimals
Terminating decimals end after a finite number of places; repeating fractions require rounding for display. The fraction remains the exact representation when the decimal repeats.
The undefined zero denominator
A denominator of zero is undefined. It cannot be interpreted as zero percent or an infinitely large ordinary number.
- The denominator is non-zero.
- Numerator and denominator describe one mathematical fraction.
- Repeating decimals are rounded to the displayed precision.
Calculations related to fraction to decimal
The following tools examine neighbouring parts of the same calculation without changing the inputs or assumptions used above.
Quick answers
Frequently asked questions
How do I convert a fraction to a decimal?
Divide the numerator by the denominator.
How do I convert the fraction to a percentage?
Divide numerator by denominator and multiply the result by 100.
What is the reciprocal of a fraction?
It swaps the numerator and denominator, provided the original numerator is not zero.
Educational content only. This guide is not financial advice.