Page 325 - Basic College Mathematics with Early Integers

302 C HAPTE R 4 I DECIMALS

Concept Check True or false? The number of decimal places in the prod-
uct of 0.261 and 0.78 is 6. Explain.

PRACTICE 3 Example 3 Multiply: (-2.6)(0.8)
Multiply: (5.4)(-1.3)
Solution: Recall that the product of a negative number and a positive number is
a negative number.
(-2.6)(0.8) =-2.08

Work Practice 3

Objective Estimating when Multiplying Decimals

Just as for addition and subtraction, we can estimate when multiplying decimals to
check the reasonableness of our answer.

PRACTICE 4 Example 4 Multiply: 28.06 * 1.95. Then estimate to see whether the answer
Multiply: 30.26 * 2.98. Then is reasonable by rounding each factor, then multiplying the
estimate to see whether the rounded numbers.
answer is reasonable.
Solution:
Exact Estimate 1 Estimate 2

28.06 28 Rounded to ones or 30 Rounded to tens
* 1.95 * 2 * 2
14030 56 60
252540
280600
54.7170
The answer 54.7170 is reasonable.

Work Practice 4

As shown in Example 4, estimated results will vary depending on what esti-
mates are used. Notice that estimating results is a good way to see whether the
decimal point has been correctly placed.

Objective Multiplying Decimals by Powers of 10

There are some patterns that occur when we multiply a number by a power of 10
such as 10, 100, 1000, 10,000, and so on.

23.6951*10=236.951 Move the decimal point 1 place to the right.

1 zero
Answers
23.6951*100=2369.51 Move the decimal point 2 places to the right.
3. -7.02 4. Exact: 90.1748 Copyright 2012 Pearson Education, Inc.
2 zeros
Concept Check Answer
false: 3 decimal places and 2 decimal 23.6951*100,000=2,369,510. Move the decimal point 5 places to the right (insert a 0).
places means 5 decimal places in the
product 5 zeros