Notes
Converting Between Decimals, Fractions, and Percents
Fraction to Decimal
Remember that fractions are division. For example:
Try these examples:
3
=
4
2
=
7
Percent to Decimal
If percent means “out of one hundred” then 27% means 27 out of 100 or
27
so 0.27. Divide the percent by one
100
hundred for the equivalent decimal. Try these examples:
104% =
0.5% =
Decimal to Percent
Multiply the decimal by one hundred. For example: 0.23 = 0.23 × 100 = 23%. Try these examples:
2.34 =
0.0097 =
Terminating Decimal to Fraction
Any terminating decimal can be converted to a fraction by counting the number of decimal places, and putting the
decimal's digits over a multiple of ten. For example 2.5 =
25 5
 .
10 2
Try these examples:
1.5 =
10.2
0.0003 =
Percent to Fraction
Use the fact that "percent" means "out of a hundred". Convert the percent to a decimal, and then to a fraction. For
example 40% = 0.40 =
40
40
4 2
then reduce

 .
100
100 10 5
©Dr Barbara Boschmans
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Notes
Try these examples:
104% =
0.5% =
33
1
%=
3
12
1
%=
2
Non-terminating, Repeating Decimal to Fraction
In the case of a non-terminating, repeating decimal, the following procedure is used. Suppose you have a number
like 0.333333.... This number is equal to some fraction; call this fraction "x". That is:
Let x = 0.333333...
There is one repeating digit in this decimal, so multiply x by 10 to bring one repeating part in front of the decimal:
Then 10 x = 3.33333...
Subtract:
So
10 x = 3.33333...
- x = 0.33333...
9x=3
x=
3 1

9 3
You might have already known that
0.3 
1
from previous experiences, but it is an example to show you the
3
procedure of converting a non-terminating, repeating decimal to a fraction.
Let’s do another example: Suppose you have a number like 0.5777777.... This number is equal to some fraction; call
this fraction "x". That is:
Let x = 0.5777777...
There is one repeating digit in this decimal, so multiply x by 100 to bring the non-repeating part and the repeating
part in front of the decimal:
Then 100 x = 57.77777...
Subtract:
Then
So
100 x = 57.777777...
- 10 x = 5.7777777...
90 x = 52
[Remember: your goal is to eliminate the repeating decimal part so
subtracting x would not do this, but subtraction 10 x will!]
90 x = 52
x=
52 26

90 45
©Dr Barbara Boschmans
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Notes
Try these examples:
0.777777….. =
0.2525252525…. =
2.345345345…. =
0.45666666…. =
0.00022222…. =
©Dr Barbara Boschmans
3/5
Notes
Fraction to Percent
Convert to a decimal and then to a percent if you have a terminating decimal. For example:
Try these examples:
3
=
2
5
=
8
For non-terminating decimals you use a fraction inside the percent. For instance:
So 0.38888888… = 38.888888…%. The goal is to convert 0.888888… to a fraction, using the technique of
converting non-terminating, repeating decimals to fractions.
Let x = 0.888888...
There is one repeating digit in this decimal, so multiply x by 10 to bring one repeating part in front of the decimal:
Then 10 x = 8.88888...
Subtract:
So
10 x = 8.88888...
- x = 0.88888...
9x=8
x=
8
9
So the final answer:
7
8
 38 %
18
9
Here's a messier example:
This is non-terminating, so 0.5428571428571… = 54.28571428571% and you want to convert the 0.2857142857 to
a fraction. You can also do this by decimal long division:
Note that the remainder is 10 and the divisor is 35, so the decimal answer is:
©Dr Barbara Boschmans
4/5
Notes
Try these examples:
89
=
37
297
=
81
421
=
23
37
=
89
©Dr Barbara Boschmans
5/5