Decimal equivalents: Tenths and hundredths

In a nutshell

Tenths, hundredths and even thousandths can be easily converted to decimals using place value columns.

Simple conversions

Tenths, hundredths and thousandths are examples of simple fractions that, along with a few others, can easily be converted to decimals. It's worth learning these off by heart.

NAME	FRACTION	DECIMAL
One quarter	$\dfrac{1}{4}$	$0.25$
One half	$\dfrac{1}{2}$	$0.5$
Three quarters	$\dfrac{3}{4}$	$0.75$
One tenth	$\dfrac{1}{10}$	$0.1$
One hundredth	$\dfrac{1}{100}$	$0.01$
One thousandth	$\dfrac{1}{1000}$	$0.001$

Converting using place value

Using the denominator can help you decide which place value columns the numerator's digits should be placed in the decimal form.

From fractions to decimals

Where the denominator is $10$ :	Place the ones digit of the numerator in the tenths column and place every other digit to the left.
Where the denominator is $100$ :	Place the ones digit of the numerator in the hundredths column and place every other digit to the left.
Where the denominator is $1000$ :	Place the ones digit of the numerator in the thousandths column and place every other digit to the left.

Example 1

Convert $\dfrac{5}{10}$ to a decimal.

The numerator is $5$ - place $5$  in the tenths column.

$\begin{array}{cccc}&\text{O} & \text{.} & \text{Tth} & \text{Hth} &\text{Thth} \\&& . & 5 & \\ \end{array}$

Fill in the ones column with zero as is necessary.

$\dfrac{5}{10}=\underline{0.5}$

Example 2

Convert $\dfrac{189}{100}$ to a decimal.

The numerator is $189$ .

Place the $9$ in the hundredths column and place the other digits to the left.

$\begin{array}{cccc}&\text{O} & \text{.} & \text{Tth} & \text{Hth} &\text{Thth} \\&1& . & 8 & 9 \\ \end{array}$

$\dfrac{189}{100}=\underline{1.89}$

Note: Sometimes you might need to use equivalent fractions to get the denominator of a fraction to be $10,100$ or $1000$ !

From decimals to fractions

Converting from decimals to fractions is very similar.

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: use $10$ .
For hundredths: use $100$ .
For thousandths: use $1000$ .

Example 3

Convert $0.28$ to a fraction.

Identify the place value column of the $8$ .

$\begin{array}{cccc}&\text{O} & \text{.} & \text{Tth} &\underline{\text{Hth}} \\&0& . & 2&8 \\ \end{array}$

Write as a fraction with $28$ in the numerator and $100$ in the denominator.

$0.28=\underline{\dfrac{28}{100}}$