Converting decimals to fractions

​​In a nutshell

Decimals and fractions are often used alongside each other and it's important to be able to convert between the two - with and without a calculator.

Decimals to fractions

Procedure

Example 1

Write $$0.24$$ as a fraction in its simplest form.

Identify the place value of the $$4$$.

$$4$$​ is in the hundredths column.

Write $$24$$ as the numerator and $$100$$ as the denominator.

$$0.24=\dfrac{24}{100}$$

​

Simplify by dividing the top and bottom by four.

$$\dfrac{24\div4}{100\div4}=\underline{\dfrac{6}{25}}$$​​

Fractions to decimals

​​With a calculator

To convert a fraction to a decimal using a calculator, simply divide the numerator by the denominator.

Example 2

Write $$\dfrac{15}{32}$$ as a decimal.

Type in $$15\div32$$ on a calculator and write down the answer.

$$15\div32=\underline{0.46875}$$​​

Without a calculator

​​Procedure

Note: Remember if the fraction is equivalent to $$\dfrac{1}{4}, \dfrac{1}{2}$$ or $$\dfrac{3}{4}$$, it can be converted to $$0.25, 0.5$$ or $$0.75$$.

Example 3

Write $$\dfrac{3}{15}$$ as a decimal.

Divide top and bottom by three.

$$\dfrac{3\div3}{15\div3}=\dfrac{1}{5}$$

Multiply top and bottom by two.

$$\dfrac{1\times2}{5\times2}=\dfrac{2}{10}$$

Place the two in the tenths column and fill in the ones column with a zero.

​$$\dfrac{3}{15}=\underline{0.2}$$