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159
CH 28  FRACTIONS, DECIMALS,
AND PERCENTS
 Introduction
Our goal in this little chapter is to give a comprehensive overview of
the connections between the three main types of numbers used in
math: fractions, decimals, and percents. First, a couple of warnings:
1.
There is to be NO rounding in this chapter; carry all divisions
out until the remainder is 0.
2.
All fractions must be reduced to lowest terms.
 Decimal to Percent
We know that the decimal number 0.27 is equal to the fraction 27
100
(because the digit 7 is in the hundredths place).
We also just learned that the 27% means 27 (since percent always
100
means “out of 100”).
Thus, since both 0.27 and 27% represent 27 , it follows that
100
0.27 = 27%.
So, to convert a decimal to a percent, move the decimal point two
places to the right and attach the percent sign.
0.2375 = 23.75%
37.3 = 3,730%
7 = 700%
Ch 28  Fractions, Decimals, and Percents
160
 Percent to Decimal
This process is exactly the opposite
of the previous one.
To convert a percent to a
decimal, move the decimal point
two places to the left and drop the
percent sign.
123.07% = 1.2307
Homework
Fraction Decimal Percent
1/2
0.25
70%
3/4
0.375
7.95% = 0.0795
279% = 2.79
87.5%
5/8
0.0625
 Fraction to Decimal
To convert a fraction to a
decimal, divide the numerator by
the denominator. Recall the TopInside-Left rule for division.
18.75%
9/16
0.52
85%
13 = 20 13 = 0.65
20
65 = 50 65 = 1.3
50
0.6
9/9
1/32
0.15625
 Decimal to Fraction
96.875%
To convert a decimal to a
fraction, write the decimal
number over the appropriate
power of 10 (determined by the
place value of the last digit), and
reduce the fraction.
13/40
0.9625
Ch 28  Fractions, Decimals, and Percents
1.875%
161
0.9 = 9
10
0.125 = 125 = 1
1,000
2.0005 = 2
8
5
= 2 1
10,000
2,000
 Percent to Fraction
To convert a percent to a fraction, write the percent number over
100 and reduce, just like we did in the chapter Introduction to
Percents.
6% =
6 = 3
100
50
78% = 78 = 39
100
50
125% = 125 = 1 25 = 1 1
100
100
4
 Fraction to Percent
To convert a fraction to a percent,
1) convert the fraction to a decimal
2) convert the resulting decimal to a percent
19 = 0.95 = 95%
20
1 = 0.00625 = 0.625%
160
Ch 28  Fractions, Decimals, and Percents
162
 Other Methods
To help you remember which way to move the decimal point when
converting between decimals and percents, we can use the Sesame
Street trick  think of the alphabet:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
To convert a Decimal to a Percent, you’re going from D to P, which is
going to the right in the alphabet, so move the decimal point two places
to the right.
Similarly, to convert a Percent to a Decimal, you’re going from P to D,
which is going to the left in the alphabet, so move the decimal point two
places to the left.
Here’s yet another way to convert between decimals and percents.
3.5%
Example:
=
3.5%
1
(anything divided by 1 is itself)
=
3.5%
100%
(since 100% = 1)
=
3.5
100
(the percents cancel out)
=
0.035
(long division, or simply move the
decimal point 2 places to the left)
0.007
Example:
=
0.007  1
(anything times 1 is itself)
=
0.007  100%
(since 100% = 1)
=
0.7%
(normal multiplication, or simply move
the decimal point 2 places to the right)
Ch 28  Fractions, Decimals, and Percents
163
Solutions
Fraction
Decimal
Percent
1/2
0.5
50%
1/4
0.25
25%
7/10
0.7
70%
3/4
0.75
75%
3/8
0.375
37.5%
7/8
0.875
87.5%
5/8
0.625
62.5%
1/16
0.0625
6.25%
3/16
0.1875
18.75%
9/16
0.5625
56.25%
13/25
0.52
52%
17/20
0.85
85%
3/5
0.6
60%
9/9
1
100%
1/32
0.03125
3.125%
5/32
0.15625
15.625%
31/32
0.96875
96.875%
13/40
0.325
32.5%
77/80
0.9625
96.25%
3/160
0.01875
1.875%
Ch 28  Fractions, Decimals, and Percents
164
“I did then what I
knew how to do.
Now that I know better,
I do better.”
 Maya Angelou
Ch 28  Fractions, Decimals, and Percents