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# Decimals Review for Armed Services Vocational Aptitude Battery (ASVAB) Study Guide

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Updated on Jun 23, 2011

A decimal is a special kind of fraction. You use decimals every day when you deal with money—\$10.35 is a decimal that represents 10 dollars and 35 cents. The decimal point separates the dollars from the cents. Because there are 100 cents in one dollar, 1¢ is of a dollar, or \$.01.

Each decimal digit to the right of the decimal point has a name:

Example:

.1 = 1 tenth =
.02 = 2 hundredths =
.003 = 3 thousandths =
.0004 = 4 ten-thousandths =

When you add zeros after the rightmost decimal place, you don't change the value of the decimal. For example, 6.17 is the same as all of these:

6.170
6.1700
6.17000000000000000

If there are digits on both sides of the decimal point (like 10.35), the number is called a mixed decimal. If there are digits only to the right of the decimal point (like .53), the number is called a decimal. A whole number (like 15) is understood to have a decimal point at its right (15.). Thus, 15 is the same as 15.0, 15.00, 15.000, and so on.

### Changing Fractions to Decimals

To change a fraction to a decimal, divide the bottom number into the top number after you put a decimal point and a few zeros on the right of the top number. When you divide, bring the decimal point up into your answer.

Example: Change to a decimal.
 1. Add a decimal point and 2 zeros to the top number (3): 3.00 2. Divide the bottom number (4) into 3.00: Bring the decimal point up into the answer: 3. The quotient (result of the division) is the answer: .75

Some fractions may require you to add many decimal zeros for the division to come out evenly. In fact, when you convert a fraction like to a decimal, you can keep adding decimal zeros to the top number forever because the division will never come out evenly. As you divide 3 into 2, you will keep getting 6's:

2 ÷ 3 = .6666666666 etc.

This is called a repeating decimal and it can be written as You can approximate it as .67, .667, .6667, and so on.

### Changing Decimals to Fractions

To change a decimal to a fraction, write the digits of the decimal as the top number of a fraction and write the decimal's name as the bottom number of the fraction. Then reduce the fraction, if possible.

Example: .018
1. Write 18 as the top of the fraction: 18
2. Three places to the right of the decimal means thousandths, so write 1,000 as the bottom number:
3. Reduce by dividing 2 into the top and bottom numbers:

1. .008
2. 3.48
3. 123.456

### Comparing Decimals

Because decimals are easier to compare when they have the same number of digits after the decimal point, tack zeros onto the end of the shorter decimals. Then all you have to do is compare the numbers as if the decimal points weren't there:

Example: Compare .08 and .1
1. Tack one zero at the end of .1:      .10
2. To compare .10 to .08, just compare 10 to 8.
3. Since 10 is larger than 8, .1 is larger than .08.