Decimals and Percents Study Guide for McGraw-Hill's ASVAB

Percents

Percent means "out of 100" or "per hundred." For example, "70%" is read as "70 percent," meaning 70 out of 100 equal parts. Percents are useful ways to show parts of a whole. They can also be easily changed into decimals or fractions.

Working with Percent   On the ASVAB, you'll probably need to know how to change percents to decimals and fractions, and how to solve problems involving percent.

Changing Percents to Decimals Percent means "per 100." So 70% means "70 per 100," which is 70/100 or 70 ÷ 100, which is 0.70. So to change percents to decimals, delete the percent sign and place the decimal point two places to the left. You may need to add zeros.

Examples

67% = 0.67

6% = 0.06 (A zero was added to the left of the 6.)

187% = 1.87

0.14% = 0.0014 (Two zeros were added to the left of the 14.)

Changing Decimals to Percents To change decimals to percents, merely move the decimal point two places to the right and add a percent sign. (You may need to add a zero on the right.)

Examples

0.67 = 67%

0.4 = 40% (A zero was added to the right of the 4.)

1.87 = 187%

28.886 = 2888.6%

0.0014 = 0.14%

Changing Percents to Fractions A percent is some number over (divided by) 100. So every percent is also a fraction with a denominator of 100. For example, 45% = .

To change percents to fractions, remove the percent sign and write the number over 100. Reduce the fraction to lowest terms.

Examples

Changing Fractions to Percents To change fractions to percents, change the fraction to a decimal and then change the decimal to a percent.

Examples

Time Savers: Fractions, Decimals, and Percents Memorizing some of these relationships might save you some calculation time.

Finding a Percent of a Number

The ASVAB Math Knowledge test and Arithmetic Reasoning test frequently include problems that ask you to find a percent of a number. Problems are often worded like this: "What is 25% of 1,000?" There are two ways you can solve this kind of problem. You can start by changing the percent into a fraction, or you can change it into a decimal.

If you change 25% into a fraction, solve the problem like this:

If you change 25% into a decimal, solve the problem like this:

0.25 × 1,000 = 250

You should use the approach that is easiest and best for you.

Percent problems are sometimes stated in another way. For example, a problem may ask, "25 is what percent of 200?" When you see a problem like this, make it into an equation:

Example

30 is what percent of 90?

You can also solve the problem by setting up a proportion:

Example

30 is what percent of 120?

Finding the Percent Increase or Decrease

You will likely also encounter these types of percent problems on the ASVAB. Here is an example: "What is the percent increase in Kim's salary if she gets a raise from $12,000 to $15,000 per year?" Set this up as an equation with the following structure

Example (Increase)

For the problem above about Kim's salary, the amount of change is 3,000 because Kim's salary increased by that amount. The original number is 12,000. Plug those numbers into the formula:

Kim's salary increased by 25%.

Example (Decrease)

A CD player has its price reduced from $250 to $200. What is the percent decrease? Use the same process as with the previous problem.

The amount of change (decrease) is 50 (250 minus 200). The original number (original price) is $250. Plug these numbers into the formula:

The CD price decreased by 20%.