Converting Between Decimals, Fractions, and Percents

[Pages:5]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

27

If percent means "out of one hundred" then 27% means 27 out of 100 or

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 then reduce 40 4 2 .

100

100 10 5

?Dr Barbara Boschmans

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Notes

Try these examples:

104% =

0.5% =

1

33 % =

3

1

12 % =

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:

10 x = 3.33333... - x = 0.33333...

9 x = 3

So

x= 31

93

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:

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!]

Then 90 x = 52

So

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:

10 x = 8.88888... - x = 0.88888...

9 x = 8

8

So

x =

9

So the final answer: 7 38 8 % 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

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