Math Help for Section 3.3, Page 118
Percents
In applications involving percents, you usually must convert the
percents to decimal (or fractional) form before performing any
arithmetic operations. So, you need to be able to convert from percents
to decimals (or fractions), and vice versa. In addition to the parts
per one hundred model given in the text on page 118, the
following
verbal model can be used to perform the conversions.
Example
1: Tip
You could do Example 1 using the above model as follows.
| a. |
$1.20 = \left( {1.20} \right)\left( {100\% } \right) = 120\% $ |
| So, the decimal 1.20 corresponds to 120%. | |
| b. | $\eqalign{{3 \over 5} = {3 \over 5}\left({100\% } \right) =& {{300} \over 5}\% \cr =& 60\% \cr}$ |
| So, the fraction ${3 \over 5}$ corresponds to 60%. |
Study
Tip
Note in Example 1(a) that it is possible to have percents that are
larger than 100%. It is also possible to have percents that are less
than 1%, such as ${1 \over 2}\% $ or 0.78%. The decimals and fractions
corresponding to
these percents are shown below.
| Percent | Decimal | Fraction | ||
| ${1 \over 2}\%$ | $\Leftrightarrow$ | $0.005$ | $\Leftrightarrow$ | $\displaystyle{1 \over {200}}$ |
| $0.78\%$ | $\Leftrightarrow$ | $0.0078$ | $\Leftrightarrow$ | $\displaystyle{{39} \over {5000}}$ |
Example
2: Check
You could check Example 2 using the above verbal model as follows.
| a. |
$0.035 = \left( {0.035} \right)\left( {100\% } \right) = 3.5\% $ |
Solution checks. ✓ |
| b. | $\eqalign{{{11} \over {20}} = {{11} \over {20}}\left( {100\% } \right) = & {{1100} \over {20}}\% \cr = & 55\% \cr} $ |
Solution checks. ✓ |
Technology
Tip
Many calculators have a function or even a specific key for converting
fractions to decimals and decimals to fractions. Calculators
often have a key that looks like this
for converting fractions to decimals or vice versa and a key
that looks like this
that converts percents to decimals. You may have to use the
key of a scientific calculator or look through the menu of a
graphing calculator to access these keys.
To do Example 2 using these
functions, you could type the following
into a scientific calculator. Note that these instructions may not
agree precisely with the steps required by your calculator.
| Keystrokes | Display | |
| a. | 3.5  |
0.035 |
| b. | 55 |
11/20 |