Q:

How do I find out 100% of a number that is only 80% of the total?

A:

Quick Answer

In order to find 100 percent of the given number that represents 80 percent of another number, divide it by 0.80. The term percent means per hundred, so 80 percent is the fraction 80/100 or 0.80 for this calculation. In American English, percent a compound word; however, the British spelling of "per cent" helps to remind the user this word's meaning, according to Reference.com.

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Full Answer

One calculates percentage by dividing the number of items by the total and multiplying by 100. If the total is t, and the number items under consideration is n, then p=(n/t)x100. Using algebra to solve the formula for t, the number the question requires, gives the following expression: t=(n/p)x100. If 8 is equal to 80 percent of the total, inserting the numbers into the equation results in provides the t=(8/80)x100 so t=10. However, knowing to convert the percentage to a decimal and divide the given number by the percentage avoids algebraic manipulation and provides the same results: t=8/0.80 or t=10.

A common mistake of novices performing these calculations is to multiply the given number by the missing figure of 20 percent and adding the result to the original number. However, this error leads to the wrong answer. In the above example, 20 percent of 8 is 1.6, which, when added to 8 is only 9.6.

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