Basic Mathematics for College Students

344 Chapter 4 Decimals

SECTION 4.3

Multiplying Decimals

Since decimal numbers are base-tennumbers, multiplication of decimals is similar to

multiplication of whole numbers. However, when multiplying decimals, there is one

additional step—we must determine where to write the decimal point in the product.

1 Multiply decimals.

To develop a rule for multiplying decimals, we will consider the multiplication

and find the product in a roundabout way. First, we write 0.3 and 0.17 as

fractions and multiply them in that form. Then we express the resulting fraction as a

decimal.

Express the decimals 0.3 and 0.17 as fractions.

Write the resulting fraction as a decimal.

From this example, we can make observations about multiplying decimals.

• The digits in the answer are found by multiplying 3 and 17.

3  17  51

• The answer has 3 decimal places. The sumof the number of decimal places in
  the factors 0.3 and 0.17 is also 3.

1 decimal 2 decimal 3 decimal

place places places

These observations illustrate the following rule for multiplying decimals.

0.3  0.17  0.051

0.3  0.17  0.051

51

0.051 1,000



51

1,000

Multiply the numerators.

Multiply the denominators.



3  17

10  100

0.30.17

3

10



17

100

0.30.17

} } }

} } }

Multiplying Decimals

To multiply two decimals:

1. Multiply the decimals as if they were whole numbers.


2. Find the total number of decimal places in both factors.


3. Insert a decimal point in the result from step 1 so that the answer has the
   same number of decimal places as the total found in step 2.

EXAMPLE (^1) Multiply:
StrategyWe will ignore the decimal points and multiply 5.9 and 3.4 as if they
were whole numbers. Then we will write a decimal point in that result so that the
final answer has two decimal places.

5.93.4

Self Check 1

Multiply:

Now TryProblem 9

2.74.3

Objectives

1 Multiply decimals.

2 Multiply decimals by powers

of 10.

3 Multiply signed decimals.

4 Evaluate exponential

expressions that have decimal

bases.

5 Use the order of operations

rule.

6 Evaluate formulas.

7 Estimate products of decimals.

8 Solve application problems by

multiplying decimals.