The percent sign $\% $ means “divided by 100.”

**Example.**

$\dfrac{3}{5} = 0.60 = \dfrac{60}{100} = 60\%$ of the circles are blue.

**Example. **$ 50\% = \dfrac{50}{100} = 0.50 = 0.5$

**Example.** $ 23.4\% = \dfrac{23.4}{100} = 0.234$

Wild raspberries near Appalachian Trail, NY.

**Question.** Suppose you conducted a survey and asked 7 people if they like raspberries. Suppose 5 out of the 7 respondents said they do. What percent of the respondents said they liked raspberries? Express your answer to the nearest tenth of a percent (see **How to Round Numbers** below).

**Answer.** Using a calculator we see that $ \dfrac{5}{7} = 0.7142857 = 71.42857\%$. So, to the nearest tenth of a percent $ \dfrac{5}{7} = 71.4\%$

**Question.** Suppose $25\%$ of the fruit in a box are spoiled. If there are 200 fruit in the box, how many fruit are spoiled?

**Answer.** $25\% \text{ of } 200 = 200 \times 0.25 = 50$.

**Question.** Suppose $20\%$ of the applicants are from New York and that $50\%$ of New Yorkers are from New York City. What percent of the applicants are from New York City?

**Answer.** $50\% \text{ of } 20\% = 0.20 \times 0.50 = 0.10 = 10\%$

**Trick to Convert a Decimal to a Percent**

To convert a decimal to a percent you move the decimal point 2 places to the right:

**Example.** $$ 0.123 = 12.3\%$$

**How to Round Numbers**

**Example.** To round 0.983 to the nearest hundredth (two decimal places) we look at the thousandth place (the third decimal place) which is the integer 3. Since 3 is less than 5 we round 0.983 down to 0.98. We might write $0.983 \approx 0.98$ the symbol $ \approx $ means “approximately”.

To round 0.986 to the nearest hundredth (two decimal places) we look at the thousandth place (the third decimal place) which is the integer 6. Since 6 is greater than or equal to 5 we round 0.983 up to 0.99. We might write $0.986 \approx 0.99$ the symbol $ \approx $ means “approximately”.

See Figure below.

**Question.** Round 2.949 to the nearest tenth (one decimal place).

**Answer.** $2.949 \approx 2.9$ because in the hundredths place we have a 4.

**Question.** Round 2.349 to the nearest hundredths (two decimal places).

**Answer.** $2.349 \approx 2.35$ because in the thousandths place we have a 9.

**Question.** Round 2.95 to the nearest tenth (one decimal place).

**Answer.** $2.95 \approx 3.0$ because in the hundredths place we have 5, so we round the 9 up to 0 (which really means round it up to 10) so the 2.95 gets rounded to 3.0.

**Question.** Round 2/3 to the nearest tenth of a percent.

**Answer.** $\dfrac{2}{3} \approx 0.6666 = 66.66\% \approx 66.7\%$

**Question.** Round 1/3 to the nearest tenth of a percent.

**Answer.** $\dfrac{1}{3} \approx 0.3333 = 33.33\% \approx 33.3\%$