Module 9: Percents Part 1

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15 Module 9: Percents Part 1 — Technical Mathematics

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Percent Basics

Percent means “per one hundred”. A percent is a ratio or fraction with a denominator of $100$ .

Exercises

During Super Bowl XLIX between the Seahawks and Patriots, $89$ out of $100$ television sets in Seattle were tuned to the game.^[1]

1. What percent of the television sets were tuned to the game?

2. What percent of the television sets were not tuned to the game?

3. What percent of the squares are shaded?

4. What percent of the squares are not shaded?

To write a percent as a fraction: drop the percent sign, write the number over $100$ , and simplify if possible.

Tip: If a percent is greater than $100\%$ , the fraction will be greater than $1$ . If a percent is less than $1\%$ , the fraction will be less than $\frac{1}{100}$ .

Exercises

Write each percent as a fraction, and simplify if possible.

5. About $71\%$ of Earth’s surface is covered by water.^[2]

6. About $1.3\%$ of Earth’s land surface is permanent cropland.^[3]

7. About $0.04\%$ of Earth’s atmosphere is carbon dioxide.^[4]

8. The worldwide number of active Facebook users in the fourth quarter of 2018 was approximately $102\%$ of the number of users in the third quarter of 2018.^[5]

To write a percent as a decimal: drop the percent sign and move the decimal point two places to the left.

Exercises

Write each percent from Exercises 5 through 8 as a decimal.

9.
$71\%$

10.
$1.3\%$

11.
$0.04\%$

12.
$102\%$

To write a decimal as a percent: move the decimal point two places to the right and insert a percent sign.

Exercises

Write each decimal number as a percent.

13.
$0.23$

14.
$0.07$

15.
$0.085$

16.
$2.5$

To write a fraction as a percent, write the fraction as a decimal by dividing the numerator by the denominator, then move the decimal point two places to the right and insert a percent sign.

Alternate method: Recall from the fractions module that if the denominator of a fraction has no prime factors other than $2$ ‘s and $5$ ‘s, then the fraction can be built up to have a denominator of $10$ , or $100$ , or $1,000$ …

Exercises

17. $7$ out of $25$ students were tardy on Wednesday. Write $\frac{7}{25}$ as a percent.

18. A package of $24$ m&m’s contained $3$ orange m&m’s. Write $\frac{3}{24}$ as a percent.

Solving Percent Problems: Finding the Amount

You may use a calculator throughout the remainder of this module.

We often use the words amount and base in a percent problem. The amount is the answer we get after finding the percent of the original number. The base is the original number, the number we find the percent of. (You may also think of the amount as the part, and the base as the whole.) We can call the percent the rate.

$\text{Amount}=\text{Rate}\cdot\text{Base}$