2.05 Converting fractions to decimals

We've already looked at how to change decimals to fractions. Now let's look at how to go the other way and change fractions to decimals.

Think about the names of the columns in our place value table: tenths, hundredths, thousandths and so on. So to change fractions to decimals, it's easiest if we have a denominator of $10,100,1000$10,100,1000 and so on (so it matches the numbers in the place value table).

Worked examples

question 1

Convert $\frac{3}{10}$310​ to a decimal.

This fraction means "three tenths," so to write it in the place value table, it would be

Let's look at another example.

question 2

Convert $\frac{47}{100}$47100​ to a decimal.

This time, we need to make sure our decimal finishes in the hundredths column, so we would write this as $0.47$0.47

 

What about when we have a denominator that is not a power of 10?

If we have a fraction with a denominator that is not a power of $10$10, the we want to convert it so it does.

So the process goes:

1) Find a number you can multiply the denominator by to make it a power of $10$10.
2) Multiply the numerator and denominator by that number.
3) Then write down just the top number, putting the decimal point in the correct spot.

 

Worked examples

question 3

Question: Convert $\frac{4}{5}$45​ to a decimal.

Think: To change the denominator to $10$10, we need to know how many tenths are in $1$1 fifth.  

Do: From our work with fractions, we know that $2$2 tenths = $1$1 fifth, so for every fifth we have (and we have $4$4 of them) that is $2$2 tenths.  So $4$4 fifths, is the same as $8$8 tenths or $0.8$0.8.  

 

Let's look at another example.

Question 4

Question: Convert $\frac{159}{300}$159300​ to a decimal.

Think: To change the denominator $100$100, we ask ourselves, how many three-hundredths are in a hundredth. The answer is $3$3.  So for every $3$3 three-hundredths we have (and we have $159$159 of them) we have $1$1 hundredth.  This means that $159$159 three-hundredths is the same as $53$53 hundredths.  What we are doing here is dividing $300$300 by $3$3. Whatever we do to the denominator, we have to do to the numerator.

Do: $\frac{159}{300}$159300​ = $\frac{53}{100}=0.53$53100​=0.53

 

Converting mixed numbers

We use the same process to convert mixed numbers.

Worked examples

question 5

Question: Convert $4\frac{567}{1000}$45671000​ to a decimal.

Think: The $4$4 belongs in the units column, then the $567$567 will come after the decimal point.

Do: $4.567$4.567

 

Question 6

Question: Write $15+\frac{4}{10}+\frac{5}{1000}$15+410​+51000​

Think: Where these numbers belong in the place value table (look- we have no hundredths).

Do: $15.405$15.405

 

We may need to do some conversion or even addition before we write a decimal.

Question 7

Question: Write $4+\frac{4}{5}+\frac{15}{100}$4+45​+15100​

Think: This would be $4+\frac{8}{10}+\frac{15}{100}$4+810​+15100​. In $\frac{15}{100}$15100​, the one belongs in the tenths column, so we will have to add this on to our other tenths. In other words, we could think of it as $4+\frac{8}{10}+\frac{1}{10}+\frac{5}{100}$4+810​+110​+5100​

Do: $4.95$4.95

 

Practice questions

Question 8

Question 9

Question 10

Question 11