# Convert fraction to decimal

Before learning about how to convert fraction to decimal, please read the primer on fractions and the primer on decimal numbers.

If you can divide whole numbers, you can convert fraction to decimal - you just need to remember the decimal point!

Let's start with a simple example - convert 1/2 into a decimal (i.e. divide 1 by 2). What are the steps involved?

2 divides into 1 zero times remainder one. As shown in the diagram, write the zero from zero times above the 1 and carry the remainder one over to the 0 after the decimal point to make 10.

Now 2 divides into 10 exactly five times, so write 5 above the 10.

The fraction 1/2 is equal to the decimal 0.5.

## What about 2/5? (i.e. divide 2 by 5) 5 divides into 2 zero times remainder two. As shown above, write the zero from zero times above the 2 and carry the remainder two over to the 0 after the decimal point, making 20.

Now 5 divides into 20 exactly four times, therefore write 4 above the 20.

2/5 equals 0.4.

## Next consider 7/2 (i.e. divide 7 by 2) 2 divides into 7 three times remainder one. As shown in the diagram, write the three from three times above the 7 and carry the remainder one over to the 0 after the decimal point to make 10.

Now 2 divides into 10 exactly five times, so write 5 above the 10.

7/2 is equal to 3.5.

## How about 1/3? (i.e. divide 1 by 3) 3 divides into 1 zero times remainder one. As shown above, write the zero from zero times above the 1 and carry the remainder one over to the first 0 after the decimal point, making 10.

Now 3 divides into 10 three times remainder one. Write the three from three times above the 10 and carry the remainder one over to the second 0 after the decimal point to make 10.

Again 3 divides into 10 three times remainder one and this pattern continues so that you end up with a recurring 3 (i.e. the digit 3 repeats forever).

1/3 = 0.333333333... which can also be written to indicate that 3 recurs.

This is an example of a decimal which is recurring and does not terminate (unlike the previous examples 0.5, 0.4 and 3.5 which do terminate).

## Last let's look at 3/7 (i.e. divide 3 by 7) 7 divides into 3 zero times remainder three. As shown in the diagram, write the zero from zero times above the 3 and carry the remainder three over to the first 0 after the decimal point, making 30.

Now 7 divides into 30 four times remainder two. Write the four from four times above the 30 and carry the remainder two over to the second 0 after the decimal point to make 20.

Next 7 divides into 20 two times remainder six. Write the two from two times above the 20 and carry the remainder six over to the third 0 after the decimal point, making 60.

Then 7 divides into 60 eight times remainder four. Write the eight from eight times above the 60 and carry the remainder four over to the fourth 0 after the decimal point to make 40.

If you keep going, you end up with 3/7 = 0.428571428... - a decimal which neither recurs nor terminates!

## Are you ready to start converting fraction to decimal yourself?

You can see that some fractions convert to decimals neatly, while others convert to decimals which don't terminate!

Grab a pen and paper and try converting the following fractions

1/4               1/6               3/8               5/16               13/18

The correct answers in order are

0.25            0.1666...       0.375            0.3125            0.7222...

Notice how you end up with a recurring 6 when converting 1/6 to a decimal and a recurring 2 when converting 13/18 to a decimal.

5/16 has a double digit denominator but you can convert this fraction to decimal using the same method as before. 16 divides into 5 zero times remainder five. As shown above, write the zero from zero times above the 5 and carry the remainder five to the first 0 after the decimal point, making 50.

Next 16 divides into 50 three times remainder two. Write the three from three times above the 50 and carry the remainder two to the second 0 after the decimal point. Now try to work out the rest of the conversion yourself.

13/18 has a double digit numerator and a double digit denominator but again apply the same technique to convert to a decimal. 18 divides into 13 zero times remainder 13. As shown in the diagram, write the zero from zero times above the 3 (of 13) and carry the remainder 13 to the first 0 after the decimal point to make 130.

Next 18 divides into 130 seven times remainder four. Write the seven from seven times above the 130 and carry the remainder four to the second 0 after the decimal point. Again try to work out the rest yourself. Remember you should end up with a recurring 2!

## Moving on!

Move on now to create your own fraction to decimal chart and save having to repeatedly work out decimal equivalents of fractions. You'll also learn how to use your calculator to convert fraction to decimal which can sometimes make things much easier!

For more on fractions click:

What is a fraction?

Equivalent fractions

Simplifying fractions

How to subtract fractions

Multiplying fractions

How to divide fractions

Improper fractions

Comparing fractions

Ordering fractions

Fraction to decimal chart

Decimal to fraction

Fraction to percent