Lesson 9: Working with Decimals
Fractions and decimals are related. Every fraction has a decimal equivalent, and every decimal has a
fraction equivalent. In other words, a fraction can be written as a decimal, and a decimal can be written
as a fraction. Often times, numerical representation of a specific value is given in a decimal form—most
commonly, money. For example, two dollars and fifteen cents written in decimal form is $2.15.
Lesson Objectives
After completing this lesson, you will be able to:



Define a decimal.
Describe the relationship among decimals, fractions, and percents.
Solve simple problems involving decimals.
Place Values
Since you are certainly familiar with money, that means you have dealt with decimals a lot more than
you think you have. Like fractions, decimals show parts of a whole. In our example of 2.15, the 2
represents two parts of a unit (in this case, dollars). The.15 represents a part of a unit. What amount is
being represented? Fifteen percent (15%) of the whole is being represented. We could also write this as
a fraction: 15/100. If you divide the numerator (15) by the denominator (100), you will obtain the
decimal equivalent of the fraction 15/100. The result of this division is 0.15. This is read as “fifteen
hundredths.”
Every number in our number system has what is called a place value. Our number system is based on
tens. Each place value is ten times greater than the place value to its left, like this:
Millions
2
Hundred
thousands
5
Ten
thousands
4
Thousands
Hundreds
Tens
Ones
3
1
9
2
[decimal
point]
An example is included in the table. This number is written 2,543,192. It is read as “two million, five
hundred forty-three thousand, one hundred and ninety two.”
Values that include decimals represent place values that occur to the right of the ones value, or after the
decimal point. Each place value is ten times smaller than the place value to its left, like this:
Ones
2
3
[decimal
point]
Tenths
Hundredths
1
3
5
6
Thousandths
Ten
thousandths
Etc.
When reading a decimal, read the value to the left of the decimal point as you would read any whole
number, read the decimal point itself as the word “and,” then add the numbers to the right of the
decimal point. These are read as a whole number, with one extra step. At the end, attach the name of
the place value of the last number. In our example, 2.15 is read as “two and fifteen hundredths.” The
second example is read as “three and thirty-six hundredths.”
Decimals represent part of a whole number. Back to our first example of 2.15, the .15 is part of a whole
number. A dollar is made up of 100 cents. How much is fifteen percent of one whole dollar? Fifteen
cents. Once again, the relationship between a fraction, decimal, and percent follows:
.15 = 15/100 = 15%
Addition and Subtraction of Decimals
When adding or subtracting decimals, follow the basic rules for adding and subtracting whole numbers.
The only difference is that you must be sure to line up the decimal points of the values you are adding or
subtracting. Then you must carry the decimal point to the right place in the answer.
Here is an example:
125.4 + 13.2 would be set up like this:
125.4
+ 13.2
138.6
Notice that the decimal points are lined up. The values in each column are added together. Then the
decimal point is kept in the same position: it is “brought down” into the sum of the two numbers.
Multiplication and Division of Decimals
When multiplying decimals, follow the basic rules for multiplying whole numbers. The easiest way to
multiply a decimal is to ignore the decimal point and multiply the numbers as you normally would. Then,
add the decimal point to your answer. The answer must have as many decimal places as the two original
numbers combined.
Here is an example:
1.5 × .30
Multiply without decimal places: 15 × 30 = 450
Count the number of decimal places in both of the original numbers and then add the decimal. In this
example, there are three decimal places. So, the product has three decimal places: .450
Here is a more complex example:
32.4 × 21.2
Set the problem up vertically like this:
32.4
× 21.2
648
3240
+ 64800
686.88
Notice that as you multiply, you keep the place values aligned to each other by adding zeroes (0). This
helps you to maintain the correct number of places for your decimal.
When dividing decimal numbers using long division, follow the rules for dividing whole numbers.
Remember, in division:



The divisor is the number you divide by.
The dividend is the number you divide into.
The quotient is the result.
To perform the division, ignore the decimal point. Divide the dividend by the divisor. Once you have
your quotient, go back and add the decimal point to the quotient at the same location it is in the
dividend.
Here is an example:
Divide 8.1 by 6.
1.35
6 )8.1
6
21
18
30
30
0
Summary
Congratulations! Understanding and using basic mathematical concepts will help you not only in your
studies, but also in your day-to-day life. Just think for a minute how often you use math on any given
day. You might be grocery shopping, paying bills, or calculating your vacation time at work. All of these
tasks (and many others!) are easier if you know the basics of math.
As you move forward in your studies, be patient with yourself and look for opportunities to practice
these new skills.
Now that you’ve completed your review of fractions and decimals, complete the examination, Lessons
8-9 Examination, for this part of your course.