Page 326 - Basic College Mathematics with Early Integers

S E C T I O N 4.3 I MULTIPLYING DECIMALS AND CIRCUMFERENCE OF A CIRCLE 303

Notice that we move the decimal point the same number of places as there are
zeros in the power of 10.

Multiplying Decimals by Powers of 10 such as 10, 100,
1000, 10,000, ...
Move the decimal point to the right the same number of places as there are
zeros in the power of 10.

Examples Multiply. PRACTICE 5–7
Multiply.
5. 7.68 * 10 = 76.8 7.68
5. 23.7 * 10
6. 23.702 * 100 = 2370.2 23.702
6. 203.004 * 100
7. (-76.3)(1000) =-76,300 76.300
7. (-1.15)(1000)
Work Practice 5–7

There are also powers of 10 that are less than 1. The decimals 0.1, 0.01, 0.001,
0.0001, and so on, are examples of powers of 10 less than 1. Notice the pattern when
we multiply by these powers of 10:

569.2*0.1=56.92 Move the decimal point 1 place to the left.
1 decimal place
569.2*0.01=5.692 Move the decimal point 2 places to the left.

2 decimal places
569.2*0.0001=0.05692 Move the decimal point 4 places to the left (insert one 0).
4 decimal places

Multiplying Decimals by Powers of 10 such as 0.1, 0.01,
0.001, 0.0001, ...
Move the decimal point to the left the same number of places as there are
decimal places in the power of 10.

Examples Multiply. PRACTICE 8–10
Multiply.
8. 42.1 * 0.1 = 4.21 42.1
8. 7.62 * 0.1
9. 76,805 * 0.01 = 768.05 76,805.
9. 1.9 * 0.01
10. (-9.2)(-0.001) = 0.0092 0009.2
10. (-7682)(-0.001)
Work Practice 8–10

Many times we see large numbers written, for example, in the form 451.8 million
rather than in the longer standard notation.The next example shows us how to inter-
pret these numbers.
Answers
5. 237 6. 20,300.4 7. -1150
8. 0.762 9. 0.019 10. 7.682