Page 324 - Basic College Mathematics with Early Integers

MULTIPLYING DECIMALS AND Objectives
4.3 CIRCUMFERENCE OF A CIRCLE
Multiply Decimals.

Objective Multiplying Decimals Estimate when Multiplying
Decimals.
Multiplying decimals is similar to multiplying whole numbers.The only difference is
that we place a decimal point in the product. To discover where a decimal point is Multiply Decimals by Powers
placed in the product, let’s multiply 0.6 * 0.03. We first write each decimal as an of 10.
equivalent fraction and then multiply.
Evaluate Expressions with
6 3 18
0.6 * 0.03 = * = = 0.018 Decimal Replacement Values.
10 100 1000
c c c
Find the Circumference of Circles.
1 decimal 2 decimal 3 decimal
place places places
Solve Problems by Multiplying
Notice that 1 + 2 = 3, the number of decimal places in the product. Now let’s Decimals.
multiply 0.03 * 0.002.
3 2 6
0.03 * 0.002 = * = = 0.00006
100 1000 100,000
c c c
2 decimal 3 decimal 5 decimal
places places places
Again, we see that 2 + 3 = 5, the number of decimal places in the product.
Instead of writing decimals as fractions each time we want to multiply, we
notice a pattern from these examples and state a rule that we can use:

Multiplying Decimals
Step 1: Multiply the decimals as though they are whole numbers.

Step 2: The decimal point in the product is placed so that the number of deci-
mal places in the product is equal to the sum of the number of decimal
places in the factors.

Example 1 Multiply: 23.6 * 0.78 PRACTICE 1

Multiply: 45.9 * 0.42
Solution: 23.6 1 decimal place
μ 0.78 2 decimal places
1888
16520
18.408
Since 1+2=3, insert the
decimal point in the product so
that there are 3 decimal places.
Work Practice 1

Example 2 Multiply: 0.0531 * 16 PRACTICE 2
Multiply: 0.0721 * 48
Solution: 0.0531 4 decimal places
μ 16 0 decimal places
3186
5310
0.8496
4 decimal places (4+0=4)
Answers
Work Practice 2 1. 19.278 2. 3.4608
301