6.2: Understand Percent
- Page ID
- 114923
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- Use the definition of percent
- Convert percents to fractions and decimals
- Convert decimals and fractions to percents
Be Prepared 6.1
Before you get started, take this readiness quiz.
Translate “the ratio of to into an algebraic expression.
If you missed this problem, review Table 2.7.
Be Prepared 6.2
Write as a decimal.
If you missed this problem, review Example 5.28.
Be Prepared 6.3
Write as a fraction.
If you missed this problem, review Example 5.4.
Use the Definition of Percent
How many cents are in one dollar? There are cents in a dollar. How many years are in a century? There are years in a century. Does this give you a clue about what the word “percent” means? It is really two words, “per cent,” and means per one hundred. A percent is a ratio whose denominator is We use the percent symbol to show percent.
Percent
A percent is a ratio whose denominator is
According to data from the American Association of Community Colleges
Similarly,
Example 6.1
According to the Public Policy Institute of California
- Answer
The amount we want to convert is 44%. 44% 44% Write the percent as a ratio. Remember that percent means per 100. 44 100 44 100
Try It 6.1
Write the percent as a ratio.
According to a survey,
Try It 6.2
Write the percent as a ratio.
A study found that
Example 6.2
In
- Answer
The amount we want to convert is out of21 21 .100 100 out of21 21 100 100 Write as a ratio. 21 100 21 100 Convert the 21 per 100 to percent. 21% 21%
Try It 6.3
Write as a ratio and then as a percent: The American Association of Community Colleges reported that
Try It 6.4
Write as a ratio and then as a percent: In response to a student survey,
Convert Percents to Fractions and Decimals
Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per
How To
Convert a percent to a fraction.
- Step 1. Write the percent as a ratio with the denominator
100 . 100 . - Step 2. Simplify the fraction if possible.
Example 6.3
Convert each percent to a fraction:
- ⓐ
36% 36% - ⓑ
125% 125%
- Answer
ⓐ 36% 36% Write as a ratio with denominator 100. 36 100 36 100 Simplify. 9 25 9 25 ⓑ 125% 125% Write as a ratio with denominator 100. 125 100 125 100 Simplify. 5 4 5 4
Try It 6.5
Convert each percent to a fraction:
- ⓐ
48% 48% - ⓑ
110% 110%
Try It 6.6
Convert each percent to a fraction:
- ⓐ
64% 64% - ⓑ
150% 150%
The previous example shows that a percent can be greater than
Example 6.4
Convert each percent to a fraction:
- ⓐ
24.5% 24.5% - ⓑ
33 1 3 % 33 1 3 %
- Answer
ⓐ 24.5% 24.5% Write as a ratio with denominator 100. 24.5 100 24.5 100 Clear the decimal by multiplying numerator and denominator by 10. 24.5 ( 10 ) 100 ( 10 ) 24.5 ( 10 ) 100 ( 10 ) Multiply. 245 1000 245 1000 Rewrite showing common factors. 5 · 49 5 · 200 5 · 49 5 · 200 Simplify. 49 200 49 200 ⓑ 33 1 3 % 33 1 3 % Write as a ratio with denominator 100. 33 1 3 100 33 1 3 100 Write the numerator as an improper fraction. 100 3 100 100 3 100 Rewrite as fraction division, replacing 100 with .100 1 100 1 100 3 ÷ 100 1 100 3 ÷ 100 1 Multiply by the reciprocal. 100 3 ⋅ 1 100 100 3 ⋅ 1 100 Simplify. 1 3 1 3
Try It 6.7
Convert each percent to a fraction:
- ⓐ
64.4% 64.4% - ⓑ
66 2 3 % 66 2 3 %
Try It 6.8
Convert each percent to a fraction:
- ⓐ
42.5% 42.5% - ⓑ
8 3 4 % 8 3 4 %
In Decimals, we learned how to convert fractions to decimals. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.
How To
Convert a percent to a decimal.
- Step 1. Write the percent as a ratio with the denominator
100 . 100 . - Step 2. Convert the fraction to a decimal by dividing the numerator by the denominator.
Example 6.5
Convert each percent to a decimal:
- ⓐ
6% 6% - ⓑ
78% 78%
- Answer
Because we want to change to a decimal, we will leave the fractions with denominator
instead of removing common factors.100 100 ⓐ 6% 6% Write as a ratio with denominator 100. 6 100 6 100 Change the fraction to a decimal by dividing the numerator by the denominator. 0.06 0.06 ⓑ 78% 78% Write as a ratio with denominator 100. 78 100 78 100 Change the fraction to a decimal by dividing the numerator by the denominator. 0.78 0.78
Try It 6.9
Convert each percent to a decimal:
- ⓐ
9% 9% - ⓑ
87% 87%
Try It 6.10
Convert each percent to a decimal:
- ⓐ
3% 3% - ⓑ
91% 91%
Example 6.6
Convert each percent to a decimal:
- ⓐ
135% 135% - ⓑ
12.5% 12.5%
- Answer
ⓐ 135% 135% Write as a ratio with denominator 100. 135 100 135 100 Change the fraction to a decimal by dividing the numerator by the denominator. 1.35 1.35 ⓑ 12.5% 12.5% Write as a ratio with denominator 100. 12.5 100 12.5 100 Change the fraction to a decimal by dividing the numerator by the denominator. 0.125 0.125
Try It 6.11
Convert each percent to a decimal:
- ⓐ
115% 115% - ⓑ
23.5% 23.5%
Try It 6.12
Convert each percent to a decimal:
- ⓐ
123% 123% - ⓑ
16.8% 16.8%
Let's summarize the results from the previous examples in Table 6.1, and look for a pattern we could use to quickly convert a percent number to a decimal number.
Percent | Decimal |
---|---|
Do you see the pattern?
To convert a percent number to a decimal number, we move the decimal point two places to the left and remove the
Figure 6.3 uses the percents in Table 6.1 and shows visually how to convert them to decimals by moving the decimal point two places to the left.
Example 6.7
Among a group of business leaders,
Convert the percent to: ⓐ a fraction ⓑ a decimal
- Answer
ⓐ 77% 77% Write as a ratio with denominator 100. 77 100 77 100 ⓑ 77 100 77 100 Change the fraction to a decimal by dividing the numerator by the denominator. 0.77 0.77
Try It 6.13
Convert the percent to: ⓐ a fraction and ⓑ a decimal
Twitter's share of web traffic jumped
Try It 6.14
Convert the percent to: ⓐ a fraction and ⓑ a decimal
The U.S. Census estimated that in
Example 6.8
There are four suits of cards in a deck of cards—hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is
- ⓐ a fraction
- ⓑ a decimal
- Answer
ⓐ 25% 25% Write as a ratio with denominator 100. 25 100 25 100 Simplify. 1 4 1 4 ⓑ 1 4 1 4 Change the fraction to a decimal by dividing the numerator by the denominator. 0.25 0.25
Try It 6.15
Convert the percent to: ⓐ a fraction, and ⓑ a decimal
The probability that it will rain Monday is
Try It 6.16
Convert the percent to: ⓐ a fraction, and ⓑ a decimal
The probability of getting heads three times when tossing a coin three times is
Convert Decimals and Fractions to Percents
To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is
How To
Convert a decimal to a percent.
- Step 1. Write the decimal as a fraction.
- Step 2. If the denominator of the fraction is not
rewrite it as an equivalent fraction with denominator100 , 100 , 100 . 100 . - Step 3. Write this ratio as a percent.
Example 6.9
Convert each decimal to a percent: ⓐ
- Answer
ⓐ 0.05 0.05 Write as a fraction. The denominator is 100. 5 100 5 100 Write this ratio as a percent. 5% 5% ⓑ 0.83 0.83 The denominator is 100. 83 100 83 100 Write this ratio as a percent. 83% 83%
Try It 6.17
Convert each decimal to a percent: ⓐ
Try It 6.18
Convert each decimal to a percent: ⓐ
To convert a mixed number to a percent, we first write it as an improper fraction.
Example 6.10
Convert each decimal to a percent: ⓐ
- Answer
ⓐ 0.05 0.05 Write as a fraction. 1 5 100 1 5 100 Write as an improper fraction. The denominator is 100. 105 100 105 100 Write this ratio as a percent. 105% 105% Notice that since
the result is more than1.05 > 1 , 1.05 > 1 , 100%. 100%. ⓑ 0.075 0.075 Write as a fraction. The denominator is 1,000. 75 1,000 75 1,000 Divide the numerator and denominator by 10, so that the denominator is 100. 7.5 100 7.5 100 Write this ratio as a percent. 7.5% 7.5%
Try It 6.19
Convert each decimal to a percent: ⓐ
Try It 6.20
Convert each decimal to a percent: ⓐ
Let's summarize the results from the previous examples in Table 6.2 so we can look for a pattern.
Decimal | Percent |
---|---|
Do you see the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign.
Figure 6.5 uses the decimal numbers in Table 6.2 and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the
In Decimals, we learned how to convert fractions to decimals. Now we also know how to change decimals to percents. So to convert a fraction to a percent, we first change it to a decimal and then convert that decimal to a percent.
How To
Convert a fraction to a percent.
- Step 1. Convert the fraction to a decimal.
- Step 2. Convert the decimal to a percent.
Example 6.11
Convert each fraction or mixed number to a percent: ⓐ
- Answer
To convert a fraction to a decimal, divide the numerator by the denominator.
ⓐ Change to a decimal. 3 4 3 4 Write as a percent by moving the decimal two places. 75% 75% ⓑ Change to a decimal. 11 8 11 8 Write as a percent by moving the decimal two places. 137.5% 137.5%
ⓒ | |
Write as an improper fraction. | |
Change to a decimal. | |
Write as a percent. | |
Notice that we needed to add zeros at the end of the number when moving the decimal two places to the right.
Try It 6.21
Convert each fraction or mixed number to a percent: ⓐ
Try It 6.22
Convert each fraction or mixed number to a percent: ⓐ
Sometimes when changing a fraction to a decimal, the division continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the hundredths place. For most other cases in this book we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.
Example 6.12
Convert
- Answer
To change a fraction to a decimal, we divide the numerator by the denominator.
5 7 5 7 Change to a decimal—rounding to the nearest thousandth. 0.714 0.714 Write as a percent. 71.4% 71.4%
Try It 6.23
Convert the fraction to a percent:
Try It 6.24
Convert the fraction to a percent:
When we first looked at fractions and decimals, we saw that some fractions converted to a repeating decimal. For example, when we converted the fraction
Example 6.13
An article in a medical journal claimed that approximately
- Answer
1 3 1 3 Change to a decimal. Write as a repeating decimal. 0.333 … 0.333 … Write as a percent. 33 1 3 % 33 1 3 % We could also write the percent as
.33 . 3 _ % 33 . 3 _ %
Try It 6.25
Convert the fraction to a percent:
According to the U.S. Census Bureau, about
Try It 6.26
Convert the fraction to a percent:
According to the U.S. Census Bureau, about
Section 6.1 Exercises
Practice Makes Perfect
Use the Definition of Percents
In the following exercises, write each percent as a ratio.
In
In
The unemployment rate for those with Bachelor's degrees was
The unemployment rate in Michigan in
In the following exercises, write as
- ⓐ a ratio and
- ⓑ a percent
Convert Percents to Fractions and Decimals
In the following exercises, convert each percent to a fraction and simplify all fractions.
In the following exercises, convert each percent to a decimal.
In the following exercises, convert each percent to
- ⓐ a simplified fraction and
- ⓑ a decimal
In
In
According to government data, in
According to the U.S. Census Bureau, among Americans age
A couple plans to have two children. The probability they will have two girls is
Javier will choose one digit at random from
According to the local weather report, the probability of thunderstorms in New York City on July
A club sells
Convert Decimals and Fractions to Percents
In the following exercises, convert each decimal to a percent.
In the following exercises, convert each fraction to a percent.
In the following exercises, convert each fraction to a percent.
In the following exercises, convert each fraction to a percent.
According to the National Center for Health Statistics, in
The U.S. Census Bureau estimated that in
In the following exercises, complete the table.
Fraction | Decimal | Percent |
---|---|---|
Fraction | Decimal | Percent |
---|---|---|
Everyday Math
Sales tax Felipa says she has an easy way to estimate the sales tax when she makes a purchase. The sales tax in her city is
- ⓐ Convert
to a fraction.10% 10% - ⓑ Use your answer from ⓐ to estimate the sales tax Felipa would pay on a
dress.$95 $95
Savings Ryan has
- ⓐ Write
as a fraction.25% 25% - ⓑ Use your answer from ⓐ to find the amount that goes to savings from Ryan's
paycheck.$2,400 $2,400
Amelio is shopping for textbooks online. He found three sellers that are offering a book he needs for the same price, including shipping. To decide which seller to buy from he is comparing their customer satisfaction ratings. The ratings are given in the chart.
Use the chart to answer the following questions
Seller | Rating |
---|---|
Write seller
Write seller
Write seller
Which seller should Amelio buy from and why?
Writing Exercises
Convert
Convert
When the Szetos sold their home, the selling price was
According to cnn.com, cell phone use in
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ If most of your checks were:
…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.
…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?
…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.