Percentages are found in many contexts beyond practice problems in math textbooks. One of the best examples is sale prices, which are often advertised as a particular percentage off of a price. Tips on a restaurant bill are also usually calculated as a percentage of the total bill. Knowing how to calculate percentages is a useful skill; sometimes you'll need to know the exact percent of a number, while others only require an estimate. You can perform these calculations in your head or using a calculator.
To begin calculating a percentage, you must convert it to a decimal format by moving the decimal point two spaces to the right. For example:
- 72 percent equals 0.72
- 300 percent equals 3
- 4 percent equals 0.04
Once you have the decimal figure, multiply it by the number for which you seek to calculate the percentage; i.e., if you need to know 30 percent of 100, you convert 30 percent to a decimal (0.30) and multiply it by 100 (0.30 x 100, which equals 30).
For example, if you are told that 72 percent of all students have cell phones and there are 30 students in the class, you can figure out how many students will have cell phones by multiplying 0.72 by 30 to get 21.6.
In this example, you may need to round your answer, as you can't have 21.6 people. If you're calculating a percentage of people or animals or other things that cannot be represented by fractions, you need to round to the nearest whole number. In the example, that would be 22. Another example is that when calculating sales tax, the answer needs to be rounded to the nearest penny.
Mental Math Method
If you're at a store and quickly need to figure out the price of a sale item, you may need to learn to calculate percentages in your head. For example, if you find an item that costs $45 but is on sale for 20 percent off, you'll need to figure out how much you'll have to pay.
The first thing to do is convert the percentage into a fraction or a sum of fractions. "Percent" or "per cent" means "per hundred," so 20 percent means 20 per hundred, or 20 out of every 100. You can write it as a fraction this way: 20/100.
Then you can reduce the fraction by dividing both the top and bottom by the greatest common factor. In the above example, divide the numerator (20, the top number) and the denominator (100, the bottom number) by 20 to get 1/5.
Once you've reduced the fraction to its smallest, divide the number for which you are finding the percent by the denominator of the fraction. In the example, you would divide the $45 regular price by five, which equals nine. Then multiply nine by the numerator of the fraction (one), which equals nine. Thus, the item is $9 off and will cost $36. If the item were 40 percent off, the fraction would be 40/100, reduced to 2/5. You would then divide the price, $45, by the denominator, which is five, to equal nine. You would then multiply nine by two and get 18, which means the item is $18 off.
You can repeat these steps with multiple calculations for problems that have percentages that are not simple fractions. For example, when calculating the tip on a bill at a restaurant, you may be trying to find 15 percent of $27. Rather than converting 15 percent to 15/100 or 3/20, you can think of it as 10/100 or 1/10 and then add half of that, because it is much easier to find 1/10 than 3/20. So you would calculate 1/10 of $27, which is $2.70, plus half of that, or $1.35, to get a tip of $3.05.
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