By the end of this section, you will be able to:
How many cents are in one dollar? There are 100100 cents in a dollar. How many years are in a century? There are 100100 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 100. We use the percent symbol %, to show percent.
According to data from the American Association of Community Colleges (2015), about 57% of community college students are female. This means 57 out of every 100 community college students are female, as Figure 6.2 shows. Out of the 100 squares on the grid, 57 are shaded, which we write as the ratio 57100.
Figure 6.2 Among every 100100 community college students, 5757 are female.
Similarly, 25% means a ratio of 25/100,3% means a ratio of 3100 and 100% means a ratio of 100/100 . In words, “one hundred percent” means the total 100% is 100/100, and since 100/100=1, we see that 100% means 1 whole.
Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per 100, so the denominator of the fraction is 100
The previous example shows that a percent can be greater than 1. We saw that 125% means 125/100, or 5/4. 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 Table 6.1, 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 6 as 6.0, we can think of 6% as 6.0%.) Notice that we may need to add zeros in front of the number when moving the decimal to the left.
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.
To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100, it is easy to change that fraction to a percent.
Let’s summarize the results from the previous examples in Table 6.2 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.
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 %% 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 fractions converted to a repeating decimal. When we converted the fraction 43 to a decimal, we wrote the answer as 1.3¯. We will use this same notation, as well as fraction notation, when we convert fractions to percents in the next example.
Use the Definition of Percents
In the following exercises, write each percent as a ratio.
ⓐ a ratio and
ⓑ a percent
In the following exercises, convert each percent to a fraction and simplify all fractions.
ⓐ a simplified fraction and
ⓑ a decimal
In the following exercises, convert each decimal to a percent.
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 9.05%. She knows this is a little less than 10%.
ⓐ Convert 10% to a fraction.
ⓑ Use your answer from ⓐ to estimate the sales tax Felipa would pay on a $95 dress.
Use the chart to answer the following questions
ⓐ 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.