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

1.	Identify the place value of the last digit.
2.	Write all the digits of the decimal as the numerator.
3.	Choose the denominator based on the place value column of that last digit: For tenths: $10$ . For hundredths: $100$ . For thousandths: $1000$ .
4.	Simplify the fraction if required.

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

1.

Use equivalent fractions to get either $10,100$ or $1000$ as the denominator.

2.

Convert using the following rules:

DENOMINATOR	RULE
$10$	Place the ones digit of the numerator in the tenths column and place every other digit in order to the left.
$100$	Place the ones digit of the numerator in the hundredths column and place every other digit in order to the left.
$1000$	Place the ones digit of the numerator in the thousandths column and place every other digit in order to the left.

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.

$\dfrac{3}{15}=\underline{0.2}$