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