Math 64
7.1 "Percents, Decimals, and Fractions"
Objectives:
* Understand Percent.
* Write percents as decimals or fractions.
* Write decimals or fractions as percents.
* Applications with percents, decimals, and fractions.
Understanding Percent
The word percent comes from the Latin phrase per centum, which means "per 100." For example, 64% (64 percent)
means 64 per 100. In the square below, 64 of the 100 squares are shaded. Thus, 64% of the …gure is shaded.
Since 64% means 64 per 100, 64% is the ratio of 64 to 100,
64
:
100
64% =
64
100
:
and
Also,
De…nition:
or
Percent
kPercent means per one hundred. The "%" symbol is used to denote percent.k
Percent is used in a variety of everyday situations. For example, 58:7% of the U.S. population uses the Internet. The
store is having a 25% o¤ sale. The enrollment in community college is predicted to increase 1:3% each year.
Example 1: (Understanding percent)
A basketball player makes 81 out of 100 attempted free throws. What percent of free throws are made?
Example 2: (Understanding percent)
One hundred adults were asked to name their favorite sport, and the results are shown in the circle graph.
a) What sport was preferred by most adults? What percent preferred this sport?
b) What sport was preferred by the least number of adults?
What percent preferred this sport?
c) What percent of adults preferred basketball or baseball?
Page: 1
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
7.1
Writing Percents as Decimals or Fractions
Writing a Percent as a Decimal:
Replace the percent symbol with its decimal equivalent, 0:01 then multiply.
Example 3: (Writing percents as decimals)
Write each percent as a decimal.
a) 49%
b) 3:1%
c) 175%
d) 0:46%
e) 600%
f) 0:9%
Writing a Percent as a Fraction:
Replace the percent symbol with its fraction equivalent,
1
100
then multiply.
Example 4: (Writing percents as fractions)
Write each percent as a fraction or mixed number in simplest form.
a) 50%
b) 2:3%
c) 150%
d) 66 32 %
e) 12%
f) 4:5%
Writing Decimals or Fractions as Percents
Writing a Decimal or Fraction as a Percent:
kMultiply by 1 in the form of 100%:k
Example 5: (Writing decimals as percents)
Write each decimal as a percent.
a) 0:1:4
b) 1:75
c) 0:057
d) 0:5
Page: 2
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
7.1
Example 6: (Writing fractions as percents)
Write each fraction or mixed number as a percent.
1
a)
4
b)
c) 5 12
9
40
d) 6 51
Example 7: (Writing fractions as percents)
Write each fraction as a percent. Round to the nearest hundredth percent.
4
11
b)
a)
12
15
Applications with Percents, Decimals, and Fractions
Let’s summarize what we have learned so far about percents, decimals, and fractions:
Summary of Converting Percents, Decimals, and Fractions:
?
To write a percent as a decimal, replace the %
?
To write a percent as a fraction, replace the % symbol with its fraction equivalent,
?
To write a decimal or fraction as a percent,
symbol with its decimal equivalent, 0.01; then multiply.
1
; then multiply.
100
multiply by 100%:
If we let x represent a number, below we summarize using symbols:
Write a percent
Write a percent
Write a number
as a decimal:
as a fraction:
as a percent:
Example 8: (Applications)
Provincetown’s budget for waste disposal increased by 1 43 times over the budget from last year. What percent increase is
this?
Page: 3
Notes by Bibiana Lopez