Maths1 min readUpdated Apr 1, 2026

Understanding Fractions, Decimals, and Percentages

Learn exactly how fractions, decimals, and percentages relate to each other and how to convert freely between them.

Key Takeaways

  • Fractions, decimals, and percentages are just different ways to express parts of a whole.
  • To convert a fraction to a decimal, divide the top number by the bottom number.
  • To convert a decimal to a percentage, multiply by 100 (move the decimal right two places).
  • To convert a percentage to a fraction, put it over 100 and simplify.

Three Ways to View the Same Number

Depending on the context, a number might be easier to interpret as a fraction, a decimal, or a percentage. Half of a pie is clearly 1/2. Calculating change at a cash register uses decimal money, like $0.50. Pointing out battery life intuitively uses percentages, like 50%.

Fractions to Decimals

To change a fraction to a decimal, recognize that the fraction bar simply means "divided by". For 3/4, divide 3 by 4 using long division or a calculator to get 0.75.

Decimals to Percentages

The word "percent" literally translates to "for every 100". Thus, you turn a decimal into a percentage by multiplying by 100. This has the effect of moving the decimal point exactly two places to the right. So 0.75 becomes 75%.

Percentages Back to Fractions

To go in reverse, take the percentage and place it as the numerator over 100. If your percentage is 40%, write 40/100. Then simplify the fraction to its lowest terms by dividing the top and bottom by their greatest common divisor (which is 20 in this case). The answer is 2/5.

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