To average percentages, one should add up all the numbers involved, then divide the total sum by the amount of numbers added. It is best to convert the percentages to decimals first.
People can find the average of percentages by hand using a pen or pencil and paper, or with a calculator. Having the percentages written down on paper in a list format helps people stay organized and reduces the likelihood of errors as they work.
Converting Percentages to Decimals
Converting the percentages to decimals is a relatively easy process. Before starting, it helps to know that a percentage is one one-hundredth of a number, or 1/100. One hundred will always be the denominator of a percentage. To convert a percentage to a decimal, multiply the number by 100 and eliminate the percent sign. On paper, this equates to moving the decimal place two spaces to the left. People can also use a calculator to perform this step. As an example, start with two percentages, which are 70 percent and 30 percent. In decimal form, these numbers translate to .07 and .03 when divided by 100. Then, add the decimals together to get the total sum. In this case, the two decimals add up to equal 1. Divide that number by 2, which yields a result of .05, or one half. The final step is to multiple that number by 100 to bring it back to percent form. In this case, the average of the two percentages becomes 50 percent. Another way to come to the same answer is to start with the numbers in percentage form, 70 and 30, but eliminate the percent sign. The individual can then add the two numbers together and divide the total in half. In this case, the end result would also be 50 percent. Keep in mind that, when finding the average of more numbers, the dividing number increases. For example, to find the average of 70 percent, 25 percent and 5 percent, add all percentages and divide by 3.
Converting Fractions and Decimals
Just as percentages can be converted to decimals, decimals can be converted to percentages. The two can also be expressed as fractions because fractions, decimals and percentages show the same value, but they do so in different formats. A half of something, for example, is written in fraction form as 1/2. That number becomes .5 when expressed as a decimal, and it is written as 50 percent when expressed as a percent. To convert a decimal to a percent, multiply the decimal by 100 and add a percent sign. This can also be accomplished by moving the decimal point two places to the right. An example of this conversion is multiplying the decimals .02 and .08 by 100. This creates 20 and 80. Then, add a percent sign to each to indicate that they are percentages. To change a number from a fraction to a decimal, divide the top number by the bottom number, or divide the numerator by the denominator in mathematical terms. Changing from a fraction to a percentage involves dividing the numerator by the denominator, multiplying the result by 100 and adding a percent sign. Converting a decimal to a fraction is a more complicated equation.