Question

in 3 - 6, rewrite the sentence using a fraction in lowest terms in place of the percent.

1. the losing candidate received 32% of the vote.
2. there is less than a 0.01% chance that you will get all 10 of those true or false questions correct by guessing.
3. the price of gasoline rose 150% in the early part of the 21st century.
4. a difference of $\frac{1}{4}%$ in an apy can be significant.

in 7 - 10, rewrite the percent as a decimal and as a fraction in lowest terms.

1. 0.35%
2. 2.5%
3. 275%
4. $2\frac{3}{5}%$

in 11 - 14, rewrite the decimal as a percent.

1. 0.13
2. 1.35
3. 5
4. 0.0005

Explanation:

Step1: Recall percent - fraction conversion rule

To convert a percent to a fraction, write the percent as a fraction with a denominator of 100 and simplify.

Step2: Solve for 3

32% = $\frac{32}{100}=\frac{32\div4}{100\div4}=\frac{8}{25}$. The losing candidate received $\frac{8}{25}$ of the vote.

Step3: Solve for 4

0.01% = $\frac{0.01}{100}=\frac{0.01\times100}{100\times100}=\frac{1}{10000}$. There is less than $\frac{1}{10000}$ chance that you will get all 10 of those true - or - false questions correct by guessing.

Step4: Solve for 5

150% = $\frac{150}{100}=\frac{150\div50}{100\div50}=\frac{3}{2}$. The price of gasoline rose $\frac{3}{2}$ in the early part of the 21st century.

Step5: Solve for 6

$\frac{1}{4}\%=\frac{\frac{1}{4}}{100}=\frac{1}{4}\times\frac{1}{100}=\frac{1}{400}$. A difference of $\frac{1}{400}$ in an APY can be significant.

Step6: Solve for 7

0.35% = 0.0035 (decimal), 0.35%=$\frac{0.35}{100}=\frac{0.35\times100}{100\times100}=\frac{35}{10000}=\frac{35\div5}{10000\div5}=\frac{7}{2000}$ (fraction)

Step7: Solve for 8

2.5% = 0.025 (decimal), 2.5%=$\frac{2.5}{100}=\frac{2.5\times10}{100\times10}=\frac{25}{1000}=\frac{25\div25}{1000\div25}=\frac{1}{40}$ (fraction)

Step8: Solve for 9

275% = 2.75 (decimal), 275%=$\frac{275}{100}=\frac{275\div25}{100\div25}=\frac{11}{4}$ (fraction)

Step9: Solve for 10

$2\frac{3}{5}\%=\frac{13}{5}\%=\frac{\frac{13}{5}}{100}=\frac{13}{5}\times\frac{1}{100}=\frac{13}{500}$ (fraction), $2\frac{3}{5}\% = 0.026$ (decimal)

Step10: Solve for 11

0.13 = 13% (move the decimal point two places to the right)

Step11: Solve for 12

1.35 = 135% (move the decimal point two places to the right)

Step12: Solve for 13

5 = 500% (move the decimal point two places to the right)

Step13: Solve for 14

0.0005 = 0.05% (move the decimal point two places to the right)

Answer:

1. The losing candidate received $\frac{8}{25}$ of the vote.
2. There is less than $\frac{1}{10000}$ chance that you will get all 10 of those true - or - false questions correct by guessing.
3. The price of gasoline rose $\frac{3}{2}$ in the early part of the 21st century.
4. A difference of $\frac{1}{400}$ in an APY can be significant.
5. Decimal: 0.0035, Fraction: $\frac{7}{2000}$
6. Decimal: 0.025, Fraction: $\frac{1}{40}$
7. Decimal: 2.75, Fraction: $\frac{11}{4}$
8. Decimal: 0.026, Fraction: $\frac{13}{500}$
9. 13%
10. 135%
11. 500%
12. 0.05%