# Decimal Ratios

Lesson

## Expressing ratios as decimals

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.

#### Examples

##### Question 1

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 2

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.

##### question 3

Express $31.8:3180$31.8:3180 as a single decimal.

## Finding unknown values

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.

#### Examples

##### question 4

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

##### question 5

Find $a$a if $a:17=4.83$a:17=4.83

The same rule applies if there is more than one decimal.

##### Question 6

Find $a$a if  $a:7.7=54.98$a:7.7=54.98