Converting Fractions, Decimals and Percentages

Fraction to decimal

Step 1

Divide the numerator by the denominator. The fraction bar means division.

$[[frac{3}{8}]]=3[[div]]8$

Step 2

$3[[div]]8=0.375$

Check by multiplying back:

$0.375[[times]]8=3$

Decimal to fraction

Step 1

Count decimal places. Three decimal places mean thousandths.

$0.125=[[frac{125}{1000}]]$

Step 2

Divide numerator and denominator by their greatest common factor, $125$

$[[frac{125}{1000}]]=[[frac{1}{8}]]$

Do not put every decimal over a hundred. The last digit here is in the thousandths column.

Decimal to percentage

Step 1

Multiply the decimal by a hundred to find the percentage number.

$0.375[[times]]100=37.5$

Step 2

Attach the percent sign to that number.

$0.375=37.5[[%]]$

The percent sign changes the unit: $0.375[[times]]100=37.5[[%]]$ is not a valid equality.

Percentage to decimal

Step 1

Divide the percentage number by a hundred. This works even when it is smaller than one.

$0.5[[%]]=[[frac{0.5}{100}]]$

Step 2

$[[frac{0.5}{100}]]=0.005$

Check: $0.005[[times]]100=0.5$ Half of one percent is not half of the whole.

Fraction to percentage

Step 1

Divide, then multiply by a hundred to find the percentage number.

$[[frac{3}{5}]]=0.6$

Step 2

$0.6[[times]]100=60$

Step 3

$[[frac{3}{5}]]=60[[%]]$

Alternatively, make an equivalent fraction with denominator $100$:

$[[frac{3}{5}]]=[[frac{60}{100}]]$

Percentage to fraction

Step 1

Write the percentage number over a hundred.

$12.5[[%]]=[[frac{12.5}{100}]]$

Step 2

Multiply both parts by ten to remove the decimal, then simplify.

$[[frac{12.5}{100}]]=[[frac{125}{1000}]]$

Step 3

$[[frac{125}{1000}]]=[[frac{1}{8}]]$

Multiplying only the numerator would change the value.

More than one whole

Step 1

Convert the mixed number to an improper fraction.

$1[[frac{1}{4}]]=[[frac{5}{4}]]$

Step 2

Divide, then express the result per hundred.

$[[frac{5}{4}]]=1.25$

Step 3

$1.25[[times]]100=125$

Step 4

$1[[frac{1}{4}]]=125[[%]]$

A percentage can exceed a hundred. In reverse, $125[[%]]=[[frac{125}{100}]]=[[frac{5}{4}]]$; split off one whole for the mixed number.

A recurring value is not a rounded value

Step 1

An overbar marks digits that repeat forever. Here only the digit three repeats.

$[[frac{1}{3}]]=0.[[overline{3}]]$

Step 2

Keep the recurring percentage for an exact answer.

$[[frac{1}{3}]]=33.[[overline{3}]][[%]]$

Step 3

If asked for one decimal place in the percentage, use an approximation sign.

$33.[[overline{3}]][[%]][[approx]]33.3[[%]]$

The equals sign means exactly equal. A finite $33.3[[%]]$ is slightly smaller than a third. Keep exact values until the final rounding step. The next lesson explains how repeating decimals become fractions.