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n
division by 10 can be thought of as multiplication by 10 −n .For example,
5 ÷ 100 = 5 × 10 −2 =0.05
6.5 ÷ 10 = 6.5 × 10 −1 =0.65

86.37 ÷ 10000 = 86.37 × 10 −4 =0.008637
8 ÷ 100000 = 8 × 10 −5 =0.00008

The left movement of the decimal point is indicated by the negative exponent.
A caution about negative exponents:

10 −n is not anegative number!

3
Example 162. Show that −10 and 10 −3 are not equal.
Solution. The first one
3
−10 = −1000
is a negative number with a relatively large absolute value, while the second one

10 −3 =0.001

is a positive number with a relatively small absolute value.

4.6.1 Exercises
Multiply or divide each decimal by the indicated power of 10.

1. 6080.48 × 10

2. 6080.48 ÷ 10

3. 19 × 10 −1
4. 804.09 × 10 2

5. 804.09 ÷ 10 2

6. 0.0908 × 10 3

7. 0.0908 × 10 −3
3
8. 0.0908 × (−10 )
9. 38 × 10 −3

10. 260804.09 × 10 4

11. 260804.09 ÷ 10 5
12. 48.3 × 10 −3

13. What is the value, in dollars, of 5 million pennies?

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