Percents are a way of showing how two amounts compare to each other. This can be useful when working with statistics or showing how much a total has changed over time. You can convert any number to a percent by expressing it as a portion of another number; once you get the hang of it, you can make many percent conversions in your head.
Understanding What Percent Means
A percent designates how much of one quantity is made up by another quantity, and is always calculated in relation to 100. Here's a look at how that works:
Say you have 100 sheep, and you want to figure out how many of them are sheared. If 0 out of 100 sheep are sheared, then 0 percent of the sheep are sheared. If all 100 of the sheep are sheared, then 100 percent of the sheep are sheared. If half, 50, of the sheep are sheared, then 50 percent of the sheep are sheared.
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In this example, 100 is the total quantity of sheep, and the other numbers – first 0, then 100, then 50 in each of the three examples – represent the subset, or the amount that you're comparing to the total.
Calculating Percents Through Division
You don't need a total to be 100 to figure out the percent relationship between two amounts. All you need is the total quantity and the amount of the subset. To convert these numbers to a percent, divide the subset by the total, then multiply by 100.
For instance, say you have 72 books and 18 of them have green covers. To figure out what percent of the books have green covers, divide the number of green covers by the total number of books: 18 ÷ 72 = 0.25. Multiply that result by 100 to get the percent of green books:
0.25 × 100 = 25 percent
So, 25 percent of your books have green covers.
Using Percent to Find a Subset
The previous example showed the relationship between percent, the total quantity being considered, and a subset of the total. If you know the total quantity and the percent but don't know what subset the percent represents, you can use that relationship to find out the missing number. To do this, first convert the percent to a decimal by dividing it by 100. For instance, 19 percent is equal to .19. Then multiply this by the total number. The result will be your subset.
For instance, say you know that 70 percent of people in your town own cars. Your town has 15,000 residents. To find how many people own cars, convert 70 percent to a decimal and multiply it by 15,000. The decimal form of 70 is 70 ÷ 100, or 0.7. So to find the number of people, multiply 0.7 by 15,000:
0.7 × 15,000 = 10,500
So, 10,500 people in your town own cars.
Understanding Percents Greater than 100
You can also have percentages that are greater 100 percent. A percentage larger than 100 shows that the number you are comparing to a total is larger than said total quantity. This can be useful if you're comparing two different totals or showing a large increase in a number. Here's an example:
Farmer Bob has 24 cows, and Farmer Tom has 38 cows. To calculate Farmer Tom's cows as a percentage of Farmer Bob's cows, you'd follow the same procedure as with a smaller number. First divide 38 (the number of Farmer Tom's cows) by 24 (the number of Farmer Bob's cows), then multiply by 100:
38 ÷ 24 = 1.5833; 1.583 × 100 = 158.33 percent
So, Farmer Tom has 158.33 percent as many cows as Farmer Bob.
Showing How Things Change Over Time
Percents can also be used to show how much a quantity has changed over time. This is called percentage change. To calculate percentage change, you'll need the original quantity and the amount of the quantity after it has changed. You first calculate the amount of change by subtracting the original quantity from the final quantity. Then divide the amount of change by the original total and multiply by 100 to get the percentage. Percentage change can be shown by the following equation, where To is the original total and Tf is the final total. The same formula can be used regardless of whether the original total is larger than the final.
(Tf − To) ÷ To × 100 = percentage change
Say Mary had $557.00 in her bank account at the beginning of the month, and $415.00 in her bank account at the end of the month. First, subtract the original total from the final:
415 − 557 = -142
Then divide by the original total, and multiply by 100:
-142 ÷ 557 = -0.255; -0.255 × 100 = -25.5 percent
Because the percent change is negative, it shows that the percent change is a decrease. If the result had been positive, the percent change would have been an increase. So Mary's bank account has decreased by 25.5 percent.