Decimals and Percents Study Guide for McGraw-Hill's ASVAB (page 2)
A decimal is a number with one or more digits to the right of the decimal point. 0.862 and 3.12 are decimals. (Note that a zero is shown to the left of the decimal point when the decimal is between 0 and 1.)
Working with Decimals On the ASVAB, you'll probably need to know how to add, subtract, multiply, and divide decimals. You'll also need to know how to change decimals to fractions.
Adding and Subtracting Decimals To add or subtract decimals, line up the decimal points one above the other. Then add or subtract as you would normally. Place a decimal point in the answer beneath the other decimal points.
Add zeros in the blank decimal places to make this problem easier to tackle.
Multiplying Decimals To multiply decimals, follow the usual multiplication rules. Count the number of places to the right of the decimal point in each factor. Add the numbers of places. Put that many decimal places in the answer.
Dividing Decimals To divide decimals, follow the usual division rules. If the divisor (the number you are dividing by) has decimals, move the decimal point to the right as many places as necessary to make the divisor a whole number. Then move the decimal point of the dividend (the number you are dividing) that same number of places to the right. (You may have to add some zeros to the dividend to make this work.) Put the decimal point in the answer directly above the decimal point in the dividend.
Note that the decimal point is moved two places to the right in each term. The decimal point in the answer is directly above the decimal point in the dividend.
In this example, the decimal point is moved two places to the right in 1.25 to make 125. The dividend 50 can also be expressed as 50.00 (adding zeros), and moving the decimal point the same number of places to the right makes 5,000. No decimal point needs to be shown in the answer because the answer is a whole number.
Changing Decimals to Fractions Read the decimal and then write the fraction. Reduce the fraction to its lowest terms.
Changing Fractions to Decimals To change a fraction to a decimal, divide the numerator by the denominator.
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.
- 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.)
- 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.
Changing Fractions to Percents To change fractions to percents, change the fraction to a decimal and then change the decimal to a percent.
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:
- 30 is what percent of 90?
You can also solve the problem by setting up a proportion:
- 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
- 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%.
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%.
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