How to Increase a Number by a Percentage

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Math problems often require you to increase a number by a percentage. First, you find that percentage of the number, and then add it to the original number. The process is the same for all numbers and percents, and can be tweaked slightly to decrease a number by a percentage.

Convert Percent to Decimal

The first step in increasing a number by a percentage is to convert the percent to a decimal. The easiest way to do this is move the decimal point two points to the left. For example, 30 percent as a decimal is 0.3, and 50 percent as a decimal is 0.5. If you have a calculator with a percent key (%), enter your number and press % to convert the percent to a decimal (you may have to press the = key on some models). Another way to work out the decimal is to remember that 100 percent is 1, because it is the whole of something. This means 50 percent is one-half (o.5), 25 percent is one-quarter (0.25), 75 percent is three-quarters (0.75) and so on.

Work out Increase

Say you want to increase the number 10 by 50 percent. After you convert 50 percent to 0.5, work out 50 percent of 10 by multiplying 10 by 0.5. The answer is 5. On a calculator with a % key, you can type 10 × 50 % = to get the same answer.

Add the Increase

To increase 10 by 50 percent, you add the value of 50 percent, so you add 10 and 5. This gives you an answer of 15. This is what you get when you increase 10 by 50 percent.

If you want to decrease a number by a percentage, you subtract the value of the percent. In the example above, you subtract 5 from 10. The answer is 5. This is what you get when you decrease 10 by 50 percent.

Other Percentage Problems

In some math problems, you might know the percent increase or decrease and the new amount, and need to work out the original amount. For example, you know a bed with a $280 sale price has been reduced by 30 percent. To work out the original price of the bed, you have to establish what percentage of the original price the sale price is. The original price is 100 percent and 30 percent has been taken off, so the sale price is 70 percent of the original price. Divide the sale price (280) by the numerical value of 70 percent, or 0.7, to work out the original price. The answer is 400, so you know the original price of the bed was $400.

References

About the Author

Claire is a writer and editor with 18 years' experience. She writes about science and health for a range of digital publications, including Reader's Digest, HealthCentral, Vice and Zocdoc.

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