HFCC Math Lab
Arithmetic - 9
Fraction – Percent and Decimal – Percent Conversions
Part 1: Changing from Percents to Decimals
Remember: Percent means “per hundred” or “part out of a hundred”.
35
35
. So 35%
0.35 . From this example, we see that
100
100
changing from a percent to a decimal just requires us to move the decimal point two
places to the left and drop the percent sign.
Therefore 35 percent means
To change a percent to a decimal:
Move the decimal point two places to the left.
Drop the percent sign (%).
Examples: Change each percent to a decimal.
1.
82%
8 2 .%
2.
15.05%
3.
8.3%
4.
1
% 0.2%
5
0.82
1 5 .05%
0 8 .3%
0.1505
0.083
0 0 .2% 0.002
Part 2: Changing from Percents to Proper or Improper Fractions
In order to change a percent to a fraction, we need only use the fact that percent is “a part
out of a hundred”.
To change a percent to a fraction:
Put the percent over 100.
Drop the percent sign (%).
Reduce the fraction to lowest terms.
Revised 05/10
1
Examples: Change each percent to a proper or improper fraction in lowest terms.
25
100
1.
25%
3.
8%
5.
9.5%
6.
31.62%
7.
1
1
4
%
4
100
8.
2
16 %
3
8
100
1
4
2.
60%
2
25
4.
160%
9.5
100
9.5 10
100 10
31.62
100
31.62 100
100 100
1
100
4
2
3
100
16
16
95
1000
1 100
4 1
2
100
3
60
100
160
100
3
5
8
5
19
200
3162
10000
1581
5000
1 1
4 100
1
400
50 100
3
1
50 1
3 100
1
6
Part 3: Changing from Decimals to Percents
Percent means “per hundred” or “part out of a hundred”.
15
15% . From this example, we see that changing from a decimal
100
to a percent just requires us to move the decimal point two places to the right and write
the percent sign..
Therefore: 0.15
To change a decimal to a percent:
Move the decimal point two places to the right
Write the percent sign (%).
Examples: Change each decimal to a percent.
1.
0.15 0. 1 5 15.% 15%
2.
0.5 0. 5 0
3.
0.614 0. 6 1 4 61.4%
4.
0.126 0. 1 2 6 12.6%
Revised 05/10
2
50.% 50%
5.
0.01 0. 0 1 1.% 1%
6.
1 1. 0 0 100.% 100%
7.
0.005 0. 0 0 5 0.5%
8.
0.234 0. 2 3 4%
9.
3.46 3. 4 6
10.
5.01 5. 0 1
346.% 346%
23.4%
501.% 501%
Part 4: Changing from Proper or Improper Fractions to Percents
From example 6 above, we saw that 1 = 100%. In addition, we know that
any number
the same number. Therefore, to change
1
3 100
% 60% . From this example, we see
5 1
100
that changing a fraction to a percent requires that we multiply the fraction by 100
1
and write the percent sign.
do the following:
3
5
3
to a percent, we could
5
3
3
1
100%
5
5
To change a fraction to a percent:
Multiply the fraction by
100
.
1
Write the percent sign (%).
Examples: Change each fraction to a percent.
1.
1
2
1 100
% 50%
2 1
2.
3
4
3 100
% 75%
4 1
3.
3
10
3 100
% 30%
10 1
4.
4
3
4 100
1
% 133 %
3 1
3
5.
3
6.
3
8
3 100
% 37.5%
8 1
Revised 05/10
1
4
3
1 100
13 100
%
% 325%
4 1
4
1
3
Exercises:
Change each percent to a decimal.
1.
38%
2.
15%
3.
75.6%
4.
152%
5.
9%
6.
11.5%
7.
3.4%
8.
0.5%
9.
3
%
4
10.
1
2 %
2
Change each percent to a proper or improper fraction in lowest terms.
11.
20%
12.
62%
13.
41%
14.
26.4%
15.
1
83 %
3
16.
0.54%
17.
16.32%
18.
5
15 %
6
19.
0.05%
20.
125%
Change each decimal to a percent.
21.
0.45
22.
0.86
23.
0.11
24.
0.08
25.
6.32
26.
0.065
27.
0.222
28.
1.06
29.
0.015
30.
2
Revised 05/10
4
Change each fraction to a percent.
31.
1
4
32.
5
8
33.
8
10
34.
1
3
35.
3
5
36.
2
3
37.
1
38.
2
39.
1
9
40.
1
5
1
8
4
7
Answers to odd-numbered exercises and solutions to even-numbered exercises:
1.
0.38
2.
15%
3.
0.756
4.
152% 15 2 .% 1.52
5.
0.09
6.
11.5%
7.
0.034
8.
0.5%
0 0 .5%
9.
0.0075
10.
2
1
2
2.5%
11.
1
5
12.
62% =
13.
41
100
14.
26.4% =
26.4 26.4 10
100 100 10
15.
5
6
16.
0.54% =
0.54 0.54 100
100 100 100
Revised 05/10
5
1 5 .%
0.15
1 1 .5% 0.115
0.005
0 2.5% 0.025
62 31
100 50
264 33
1000 125
54
10000
27
5000
5
6
100
15
17.
102
625
18.
5
15 %
6
19.
1
2000
20.
125% =
21.
45%
22.
0.86 0. 8 6
86%
23.
11%
24.
0.08 0. 0 8
8%
25.
632%
26.
0.065 0. 0 6 5 6.5%
27.
22.2%
28.
1.06 1. 0 6 106%
29.
1.5%
30.
2
2. 0 0
31.
25%
32.
5
8
5 100
% 62.5%
8 1
33.
80%
34.
1
3
1 100
1
% 33 %
3 1
3
35.
60%
36.
2
3
2 100
2
% 66 %
3 1
3
37.
112.5%
38.
2
39.
11
1
9
40.
1
5
Revised 05/10
6
4
7
2
15
5
100
6
95 1
6 100
19
120
125 5
100 4
200%
4 100
18 100
1
%
% 257 %
7 1
7
1
7
1 100
% 20%
5 1