Decimals Review for Armed Services Vocational Aptitude Battery (ASVAB) Study Guide (page 4)
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:
.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:
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.
- Write 18 as the top of the fraction: 18
- Three places to the right of the decimal means thousandths, so write 1,000 as the bottom number:
- Reduce by dividing 2 into the top and bottom numbers:
Change the following decimals or mixed decimals to fractions.
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
- Tack one zero at the end of .1: .10
- To compare .10 to .08, just compare 10 to 8.
- Since 10 is larger than 8, .1 is larger than .08.
Adding and Subtracting Decimals
To add or subtract decimals, line them up so their decimal points are even. You may want to tack on zeros at the end of shorter decimals so you can keep all your digits evenly lined up. Remember, if a number doesn't have a decimal point, then put one at the end of the number.
Example: 1.23 + 57 + .038
|Line up the numbers like this:|
Example: 1.23 – .038
|Line up the numbers like this:||1.230|
Try these addition and subtraction problems:
- .905 + .02 + 3.075
- .025 + 9 + .4
- 3.48 – 2.573
- 123.456 – 122
- A park ranger drove 3.7 miles to the state park. He then walked 1.6 miles around the park to make sure everything was all right. He got back into the car, drove 2.75 miles to check on a broken light and then drove 2 miles back to the ranger station. How many miles did he drive in total?
- The average number of emergency room visits at City Hospital fell from 486.4 per week to 402.5 per week. By how many emergency room visits per week did the average fall?
To multiply decimals, ignore the decimal points and just multiply the numbers. Then count the total number of decimal digits (the digits to the right of the decimal point) in the numbers you are multiplying. Count off that number of digits in your answer beginning at the right side and put the decimal point to the left of those digits.
Example: 215.7 × 2.4
|Multiply 2,157 times 24:|
|Because there are a total of 2 decimal digits in 215.7 and 2.4, count off 2 places from the right in 51768, placing the decimal point to the left of the last 2 digits:||517.68|
If your answer doesn't have enough digits, tack zeros on to the left of the answer.
Example: .03 × .006
- Multiply 3 times 6: 3 × 6 = 18
- You need 5 decimal digits in your answer, so tack on 3 zeros: 00018
- Put the decimal point at the front of the number (which is 5 digits in from the right): .00018
You can practice multiplying decimals with these problems.
- .05 × .6
- .062 × 7.3
- 38.1 × .0184
- Joe earns $14.50 per hour. Last week he worked 37.5 hours. How much money did he earn that week?
- Nuts cost $3.50 per pound. Approximately how much will 4.25 pounds of nuts cost?
To divide a decimal by a whole number, set up the division and immediately bring the decimal point straight up into the answer Then divide as you would normally divide whole numbers:
To divide any number by a decimal, there is an extra step to perform before you can divide. Move the decimal point to the very right of the number you are dividing by, counting the number of places you are moving it. Then move the decimal point the same number of places to the right in the number you are dividing into. In other words, first change the problem to one in which you are dividing by a whole number.
- 1. Because there are two decimal digits in .06, move the decimal point two places to the right in both numbers and move the decimal point straight up into the answer:
- 2. Divide using the new numbers:
Under certain conditions, you have to tack on zeros to the right of the last decimal digit in a number you are dividing into:
- if there aren't enough digits for you to move the decimal point to the right
- if the answer doesn't come out evenly when you do the division
- if you are dividing a whole number by a decimal, you will have to tack on the decimal point as well as some zeros.
Try your skills on these division problems:
- If James Worthington drove his truck 92.4 miles in 2.1 hours, what was his average speed in miles per hour?
- Mary Sanders walked a total of 18.6 miles in 4 days. On average, how many miles did she walk each day?
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