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Percent means “for each hundred," or "for every hundred."
The symbol % is used to represent the word percent.
The ratio 26 to 100 can be written as 26%. We read 26% as "twenty-six percent."
The ratio $\frac{\text{165}}{\text{100}}$ can be written as 165%.
We read 165% as "one hundred sixty-five percent."
The percent 38% can be written as the fraction $\frac{\text{38}}{\text{100}}$ .
The percent 210% can be written as the fraction $\frac{\text{210}}{\text{100}}$ or the mixed number $2\frac{\text{10}}{\text{100}}$ or 2.1.
Since one dollar is 100 cents, 25 cents is $\frac{\text{25}}{\text{100}}$ of a dollar. This implies that 25 cents is 25% of one dollar.
Write the percent 83% as a ratio in fractional form.
$\frac{\text{83}}{\text{100}}$
Write the percent 362% as a ratio in fractional form.
$\frac{\text{362}}{\text{100}}\text{or}\frac{\text{181}}{\text{50}}$
Since a percent is a ratio, and a ratio can be written as a fraction, and a fraction can be written as a decimal, any of these forms can be converted to any other.
Before we proceed to the problems in [link] and [link] , let's summarize the conversion techniques.
To Convert a Fraction | To Convert a Decimal | To Convert a Percent |
To a decimal: Divide the numerator by the denominator | To a fraction: Read the decimal and reduce the resulting fraction | To a decimal: Move the decimal point 2 places to the left and drop the % symbol |
To a percent: Convert the fraction first to a decimal, then move the decimal point 2 places to the right and affix the % symbol. | To a percent: Move the decimal point 2 places to the right and affix the % symbol | To a fraction: Drop the % sign and write the number “over” 100. Reduce, if possible. |
Convert 12% to a decimal.
$\text{12\%}=\frac{\text{12}}{\text{100}}=\text{0}\text{.}\text{12}$
Note that
The % symbol is dropped, and the decimal point moves 2 places to the left.
Convert 0.75 to a percent.
$0\text{.}\text{75}=\frac{\text{75}}{\text{100}}=\text{75\%}\text{}$
Note that
The % symbol is affixed, and the decimal point moves 2 units to the right.
Convert $\frac{3}{5}$ to a percent.
We see in [link] that we can convert a decimal to a percent. We also know that we can convert a fraction to a decimal. Thus, we can see that if we first convert the fraction to a decimal, we can then convert the decimal to a percent.
$\frac{3}{5}\to \begin{array}{c}\hfill .6\\ \hfill 5\overline{)3.0}\\ \hfill \underline{30}\\ \hfill 0\end{array}$ or $\frac{3}{5}=0\text{.}6=\frac{6}{\text{10}}=\frac{\text{60}}{\text{100}}=\text{60\%}\text{}$
Convert 42% to a fraction.
$\text{42\%}\text{}=\frac{\text{42}}{\text{100}}=\frac{\text{21}}{\text{50}}$
or
$\text{42\%}\text{}=0\text{.}\text{42}=\frac{\text{42}}{\text{100}}=\frac{\text{21}}{\text{50}}$
Convert $\frac{3}{\text{11}}$ to a percent.
$\text{27}\text{.}\overline{\text{27}}\text{}$ %
For the following 12 problems, convert each decimal to a percent.
For the following 10 problems, convert each percent to a decimal.
For the following 14 problems, convert each fraction to a percent.
$\frac{3}{5}$
$\frac{1}{\text{16}}$
$\frac{\text{16}}{\text{45}}$
$\frac{\text{27}}{\text{55}}$
$\text{49}\text{.}\overline{\text{09}}$ %
$\frac{\text{15}}{8}$
$6\frac{4}{5}$
$\frac{1}{\text{200}}$
$\frac{6}{\text{11}}$
$\text{54}\text{.}\overline{\text{54}}$ %
$\frac{\text{35}}{\text{27}}$
For the following 14 problems, convert each percent to a fraction.
$55.\stackrel{\_}{5}\%$
$63.\stackrel{\_}{6}\%$
( [link] ) Find the quotient. $\frac{\text{40}}{\text{54}}\xf78\frac{7}{\text{21}}$ .
$\frac{4}{\text{45}}$
( [link] ) $\frac{3}{8}$ of what number is $2\frac{2}{3}$ ?
( [link] ) Find the value of $\frac{\text{28}}{\text{15}}+\frac{7}{\text{10}}-\frac{5}{\text{12}}$ .
$\frac{\text{129}}{\text{60}}\text{or}2\frac{9}{\text{60}}=2\frac{3}{\text{20}}$
( [link] ) Round 6.99997 to the nearest ten thousandths.
( [link] ) On a map, 3 inches represent 40 miles. How many inches represent 480 miles?
36 inches
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