Basic Mathematics for College Students

400 Chapter 4 Decimals

The rules for multiplying integers also hold for

multiplying signed decimals:

The product of two decimals with like signsis

positive, and the product of two decimals with

unlike signsis negative.

Multiply:

Find the absolute values: and

Since the decimals have like signs, the product is positive.

Multiply the absolute values,

0.03 and 4.1, to get 0.123.

Multiply:

Find the absolute values: and

Since the decimals have unlike signs, the product is negative.

Multiply the absolute values, 5.7

and 0.4, to get 2.28.

Make the final answer negative.

5.7(0.4)2.28

0 5.7 0 5.7 0 0.4 0 0.4

5.7(0.4)

(0.03)(4.1)0.123

0 0.03 0 0.03 0 4.1 0 4.1

(0.03)(4.1)

We can use the rule for multiplying a decimal by a

power of ten to write large numbers in standard

form.

Write 4.16 billionin standard notation:

Write 1 billion in standard form.

Since 1,000,000,000 has nine

zeros, move the decimal point in

4.16 nineplaces to the right.

4,160,000,000

4.161,000,000,000

4.16 billion4.161 billion

The base of an exponential expressioncan be a

positive or a negative decimal.

Evaluate:

The base is 1.5 and the exponent is 2. Write the base

as a factor 2 times.

Multiply the decimals.

Evaluate:

The base is 0.02 and the exponent is 2.

Write the base as a factor 2 times.

Multiply the decimals. The product of two

decimals with like signs is positive.

0.0004

(0.02)^2 (0.02)(0.02)

(0.02)^2

2.25

(1.5)^2 1.51.5

(1.5)^2

To evaluate a formula,we replace the letters with

specific numbers and then use the order of

operations rule.

Evaluate for and.

Replace lwith 4.9 and wwith 3.4.

Do the multiplication.

16.6 Do the addition.

9.86.8

2(4.9)2(3.4)

P 2 l 2 w

P 2 l 2 w l4.9 w3.4

Estimationcan be used to check the reasonableness

of an answer to a decimal multiplication.

Estimate by front-end rounding.

The estimate is 320. If we calculate , the product is exactly

314.13.

37 8.49

Round to the nearest ten.

Round to the nearest one.

This is the estimate.

40

 8

320

37

 8.49

37 8.49

We can use the five-step problem-solving strategyto

solve application problems that involve decimals.

See Examples 12 and 13 that begin on page 351 to review how to

solve application problems by multiplying decimals.