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2.2.7: Percents Part 1

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Sep 4, 2024
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- 2.2.6: Perimeter and Circumference
- 2.2.8: Ratios, Rates, Proportions

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Percent Basics

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

Exercises $\PageIndex{1}$

square graph showing how many people had there TV on

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?

square graph showing the amount of TV that were on in Seattle

3. What percent of the squares are shaded?

4. What percent of the squares are not shaded?

Answer

1. $89\%$

2. $11\%$

3. $47\%$

4. $53\%$

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 $\dfrac{1}{100}$ .

Exercises $\PageIndex{1}$

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]

Answer

5. $\dfrac{71}{100}$

6. $\dfrac{1.3}{100}=\dfrac{13}{1000}$

7. $\dfrac{0.04}{100}=\dfrac{1}{2500}$

8. $\dfrac{102}{100}=\dfrac{51}{50}$

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

Exercises $\PageIndex{1}$

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

9. $71\%$

10. $1.3\%$

11. $0.04\%$

12. $102\%$

Answer

9. $0.71$

10. $0.013$

11. $0.0004$

12. $1.02$

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

Exercises $\PageIndex{1}$

Write each decimal number as a percent.

13. $0.23$

14. $0.07$

15. $0.085$

16. $2.5$

Answer

13. $23\%$

14. $7\%$

15. $8.5\%$

16. $250\%$

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 $\PageIndex{1}$

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

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

Answer

17. $28\%$

18. $12.5\%$

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.

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

$A=R\cdot{B}$

Be sure to change the percent to a decimal before multiplying.

Exercises $\PageIndex{1}$

19. What is $9\%$ of $350$ ?

20. $30\%$ of $75$ is what number?

21. Find $13.5\%$ of $500$ .

22. $125\%$ of $80$ is equal to what amount?

23. What number is $40\%$ of $96.5$ ?

24. Calculate $0.5\%$ of $450$ .

Suppose you buy an electric drill with a retail price of $ $109.97$ in a city with $8.5\%$ sales tax.

25. Find the amount of the tax. Round to the nearest cent, if necessary.

26. How much do you pay in total?

Answer

19. $31.5$

20. $22.5$

21. $67.5$

22. $100$

23. $38.6$

24. $2.25$

25. $ $9.35$

26. $ $119.32$

Percent Basics

Exercises 2.2.7.1\PageIndex{1}

Exercises 2.2.7.1\PageIndex{1}

Exercises 2.2.7.1\PageIndex{1}

Exercises 2.2.7.1\PageIndex{1}

Exercises 2.2.7.1\PageIndex{1}

Solving Percent Problems: Finding the Amount

Exercises 2.2.7.1\PageIndex{1}

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Exercises $\PageIndex{1}$

Exercises $\PageIndex{1}$

Exercises $\PageIndex{1}$

Exercises $\PageIndex{1}$

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Exercises $\PageIndex{1}$