Proportions and Percentages

As we previously learned, proportions are just fractions/ratios that relate two numbers.  From proportions, we can determine trends such as slope, and determine missing values when comparing things proportionately.  There is one more way of expressing proportions, and that’s through percentages.  A percent means one part of every hundred.  In terms of fractions, percentages are always expressed with 100 as the denominator.  A percentage has a “unit” of the % sign.  Thus, 20 percent would be expressed as 20%.   Because percentages are in terms of 100, converting a percent to its decimal form merely involves moving the decimal point two places to the left like so: 

20.0% -> 0.200 

Going from a decimal to its corresponding percent involves the opposite, moving the decimal point on the decimal to two places to the right: 

0.200 -> 20.0% 

To summarize, percentages are proportions that are expressed in terms of 100 as the denominator.  Thus, to “convert” a proportion to a percent, the denominator of a proportion must equal 100, and the numerator must equal whatever the proportion is scaled by to do so.  For example, if you want the fraction 1/5 to be in terms of 100, divide 100 by 5, and then multiply 1 (the numerator) by the result.  This will get you the fraction 20/100, which is 20%.  Conversely, to get from the percentage to the fraction, remove the % sign, and put the number in the numerator with 100 at the denominator, then simplify the fraction (if possible).