Contemporary Mathematics

# 6.1Understanding Percent

Contemporary Mathematics6.1 Understanding Percent

Figure 6.2 The federal budget describes how money is spent and how money is earned. (credit: "Breakdown of revenues and outlays in 2021 US Federal budget" Wikimedia Commons, Public Domain)

### Learning Objectives

After completing this section, you should be able to:

1. Define and calculate percent.
2. Convert between percent, decimal, and fractional values.
3. Calculate the total, percent, or part.
4. Solve application problems involving percents.

### Example 6.8

#### Percent of Chemistry Majors

Cameron enrolls in a calculus class. In this class of 45 students, there are 18 chemistry majors. What percent of the class are chemistry majors?

1.
At the Fremont County fair, there were 2,532 adult visitors. Of these, 1,679 purchased the Adult Mega Pass. What percent of the adult visitors purchased the Adult Mega Pass?

### Example 6.9

#### Total Sales and Commission

Mariel makes a 20% commission on every sale she makes. One week, her commission check is for \$153.00. What were her total sales that week?

1.
Mina’s family has replaced 65% of their home’s older light bulbs with LED bulbs. If they now have 52 LED bulbs, how many total lightbulbs are in Mina’s house?

### Who Knew?

#### LED Lightbulbs

According to the energy website from the U.S. government, LED lightbulbs use at least 75% less energy than incandescent bulbs. They also last up to 25 times as long as an incandescent bulb. If lighting is a significant percent of your electrical use, replacing all incandescent bulbs with LED bulbs will significantly reduce your electric bill.

1.
What is the denominator for any percent?
2.
Convert 38.7% to decimal form.
3.
What is 68% of 280?
4.
Find the total if 41% of the total is 342. If necessary, round to two decimal places.
5.
TikTok has an estimated 80,000,000 (80 million) registered users in the United States. The population of the United States is 332,403,650. What percent of the U.S. population are registered TikTok users? If necessary, round to two decimal places.
6.
An Amazon fulfillment center needs to hire 20% more drivers. If there are currently 80 drivers, how many more drivers will be hired?

### Section 6.1 Exercises

For any answer, round to two decimal places, if necessary.

In the following exercises, rewrite the percent as a fraction
1 .
45%
2 .
9.1%
3 .
8%
4 .
673%
In the following exercises, rewrite the percent in decimal form.
5 .
18%
6 .
9%
7 .
71.2%
8 .
934%
9 .
Find 35% of 250
10 .
Calculate 83.1% of 390
11 .
Calculate 3.1% of 500
12 .
Calculate 750% of 620
13 .
If 40% of the total is 32, how much is the total?
14 .
If 3% of the total is 6.32, how much is the total?
15 .
If 150% of the total is 61.9, how much is the total?
16 .
If 18.1% of the total is 18.5, how much is the total?
17 .
13 is what percent of 40?
18 .
89 is what percent of 500?
19 .
31 is what percent of 73?
20 .
593.2 is what percent of 184.5?
21 .
36 people in a village of 150 want to install a new splashpad at the local playground. What percent of the village wants to install the new splashpad?
22 .
Mitena is enrolled in a movie appreciation course. There are 84 students (including Mitena) in the course. After having the students fill out a survey, the professor informs the students that 45.2% chose horror as their favorite movie genre. How many students in Mitena’s class chose horror as their favorite movie genre? Round off to the nearest integer.
23 .
Jadyn’s dorm has a “Rick and Morty night” every Wednesday during the semester. One Wednesday, 27 students from the dorm come to watch the TV show Rick and Morty. Jadyn knows this is 30% of the dorm’s residents. How many students reside in the dorm?
24 .
Percent Error. When performing a scientific experiment that results in quantities of some sort, such as mass in chemistry or momentum in physics, the percent error is often computed. Percent error, %$E$, is the percent by which the value obtained in an experiment, the observed value $O$, is different than the value that was expected, the expected value $E$, in the experiment. The formula is below.
$\% E = \frac{{|O - E|}}{E}$
Jim and Kelly are working on a chemistry experiment and expect the result to be 50 grams. However, their result was 48.7 grams. Find Jim and Kelly’s percent error.
25 .
Percent Error. See Exercise 24 for the definition of percent error.
Hailey and Elsbeth are using an experiment to determine Earth’s gravity. The expected value is $9.807\text{ m}/{\text{s}^2}$. Their experiment gives them a value of $9.457\text{ m}/{\text{s}^2}$. Find the percent error for Hailey and Elsbeth’s experiment.
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