Expressing ratios as decimals is a similar process to converting fractions to decimals. It can be useful to convert ratios to fractions when conceptualising these ratios.
Question: Express $35:100$35:100 as a single decimal.
Think: $35:100$35:100 is the same as $\frac{35}{100}$35100 and since the second number in the ratio (which becomes the denominator) is already a multiple of $10$10, we do not need to change any of our numbers around.
Do:
$35:100$35:100 | $=$= | $\frac{35}{100}$35100 | turn the ratio into a fraction |
$=$= | $0.35$0.35 | change the fraction into a decimal |
Let's look at a question where we don't have a multiply of $10$10 as the denominator.
Question: Express $23:4$23:4 as a single decimal.
Think: There are a few different ways to approach this question. My first step is going to be to change this ratio into a mixed number. Then I'll change it to a decimal.
Do:
$23:4$23:4 | $=$= | $\frac{23}{4}$234 | convert the ratio to a fraction |
$=$= | $5\frac{3}{4}$534 | convert to mixed number | |
$=$= | $5.75$5.75 | convert to decimal |
If you need a refresher on how to change fractions to decimals, click here.
Express $31.8:3180$31.8:3180 as a single decimal.
We've already looked at finding unknown whole values in ratios in Keeping it in Proportion. The same process applies whether we have whole numbers or decimal values.
Question: Find $b$b if $b:40=12$b:40=12
Think: This ratio means that $\frac{b}{40}=12$b40=12 , so to get b by itself, we need to multiply both sides by $40$40.
Do:
$b:40$b:40 | $=$= | $12$12 | |
$\frac{b}{40}$b40 | $=$= | $12$12 | change ratio into a fraction |
$b$b | $=$= | $12\times40$12×40 | multiply both sides by $40$40 |
$b$b | $=$= | $480$480 | evaluate |
Find $a$a if $a:17=4.83$a:17=4.83
The same rule applies if there is more than one decimal.
Find $a$a if $a:7.7=54.98$a:7.7=54.98
Use rates and ratios