Fractions, Decimals and Percentages

In a Nutshell

Fractions, decimals and percentages are three outfits for the same number. Learn to change between them.

Every fraction can be written as a decimal (divide the numerator by the denominator). Every decimal can be written as a percentage (multiply by 100). And every percentage can be written as a fraction (put it over 100 and simplify).

Here are the key conversions:

Fraction→÷Decimal→×100Percentage\text{Fraction} \xrightarrow{\div} \text{Decimal} \xrightarrow{\times 100} \text{Percentage}

The diagram below shows common equivalents side by side. Click any button to see the three forms update together.

Fractions, decimals and percentages synchronised slider A slider from 0 to 1 controls three synchronised displays: a fraction bar, a decimal readout and a 10 by 10 percentage grid. All three representations update simultaneously to show they describe the same quantity.
Snap to:

Try different values. Some fractions, like 13\frac{1}{3}, give recurring decimals. That is perfectly normal.

Watch it work

Question: Write 38\frac{3}{8} as a decimal and as a percentage.

Have a go

Q1. Write 710\frac{7}{10} as a decimal and as a percentage.

Q2. Write 0.450.45 as a fraction in its simplest form.

Q3. Write 35%35\% as a decimal and as a fraction.

Q4. Which is larger: 25\frac{2}{5} or 0.450.45?