# Percents

## Understand Percent


### 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.
According to data from the American Association of Community Colleges  about  of community college students are female. This means  out of every  community college students are female, as  shows. Out of the  squares on the grid,  are shaded, which we write as the ratio 
Similarly,  means a ratio of  means a ratio of  and  means a ratio of  In words, "one hundred percent" means the total  is  and since  we see that  means  whole.

### Convert Percents to Fractions and Decimals

Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per  so the denominator of the fraction is 
The previous example shows that a percent can be greater than  We saw that  means  or  These are improper fractions, and their values are greater than one.
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.
Let's summarize the results from the previous examples in , and look for a pattern we could use to quickly convert a percent number to a decimal number.
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  sign. (Sometimes the decimal point does not appear in the percent number, but just like we can think of the integer  as  we can think of  as ) Notice that we may need to add zeros in front of the number when moving the decimal to the left.
 uses the percents in  and shows visually how to convert them to decimals by moving the decimal point two places to the left.

### 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  it is easy to change that fraction to a percent.
To convert a mixed number to a percent, we first write it as an improper fraction.
Let's summarize the results from the previous examples in  so we can look for a pattern.
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.
 uses the decimal numbers in  and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the  sign.
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.
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.
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  to a decimal, we wrote the answer as  We will use this same notation, as well as fraction notation, when we convert fractions to percents in the next example.

### Key Concepts

1. Convert a percent to a fraction.



2. 
Convert a percent to a decimal.

3. 
Convert a decimal to a percent.

4. 
Convert a fraction to a percent.


### Practice Makes Perfect

Use the Definition of Percents 
In the following exercises, write each percent as a ratio.
In the following exercises, write as

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

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.
In the following exercises, complete the table.

### Everyday Math

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

### Writing Exercises


### 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.