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New Zealand
Level 6 - NCEA Level 1

Decimal Ratios


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.


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.


$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.


$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.


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.


$b:40$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 



Apply direct and inverse relationships with linear proportions


Apply numeric reasoning in solving problems

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