Converting fractions, decimals and percentages

Fractions, decimals and percentages are three ways to show the same thing. For every fraction, there will be an equivalent (the same) decimal and percentage.

Converting fractions to decimals

Divide the denominator by the numerator using the bus stop method.

$$\frac{3}{4}=3÷4=0.75$$

Converting decimals to fractions

Using a place value table, find the column of the last digit in the decimal and pout all the digits over this.

$$0.023$$

The last digit (the 3) is in the thousandths column, so we will put all the digits over a thousand.

$$0.023=\frac{23}{1000}$$

Converting fractions to percentages

Convert to a decimal, then multiply by 100%.

$$\frac{1}{5}=0.2$$

$$0.2\times 100=20\mathrm{\%}$$

If you get the denominator of the fraction to be 100, the numerator is the percentage.

$$\frac{1}{5}=\frac{20}{100}=20\mathrm{\%}$$

Converting percentages to fractions

Put the percentage over 100.

$$25\mathrm{\%}=\frac{25}{100}=\frac{1}{4}$$

Converting decimals to percentages

Multiply by 100%.

$$0.43\times 100\mathrm{\%}=43\mathrm{\%}$$

Converting percentages to decimals

Divide by 100.

$$53\mathrm{\%}÷100=0.53$$

Ordering

To order fractions, decimals and percentages always convert them into the same thing, normally decimals, then compare them. Don't forget to convert them back when you write your answer!