1. Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100
Bellwork
Evaluate each expression.
 1,000
 1,000
 100
 100
5. 104
6. 10–4
123,000
0.123
0.3
10,000
0.0001 1

2. Powers of Ten and Scientific Notation

3. Objectives Evaluate and multiply by powers of 10.
Convert between standard notation and scientific notation.

4. The table shows relationships between several powers of 10.
Each time you divide by 10, the exponent decreases by 1 and the decimal point moves one place to the left.

5. The table shows relationships between several powers of 10.
Each time you multiply by 10, the exponent increases by 1 and the decimal point moves one place to the right.

7. Example 1: Evaluating Powers of 10
Find the value of each power of 10.
A. 10–6
B. 104
C. 109
Start with 1 and move the decimal point six places to the left.
Start with 1 and move the decimal point four places to the right.
Start with 1 and move the decimal point nine places to the right.
10,000
1,000,000,000

8. You may need to add zeros to the right or left of a number in order to move the decimal point in that direction.
Writing Math

9. Try Problem 1
Find the value of each power of 10.
a. 10–2
b. 105
c. 1010
Start with 1 and move the decimal point two places to the left.
Start with 1 and move the decimal point five places to the right.
Start with 1 and move the decimal point ten places to the right.
0.01
100,000
10,000,000,000

10. Scientific notation is a number expressed in the form a X 10n, where 1 ≤ a < 10 and n is an integer.

11. Rewriting in Decimal Form
Rewrite in decimal form:
a.) X 103 b.) 5.6 X 1010
c.) 6.5 X d.) X 10-5

12. Rewriting in Scientific Notation
Rewrite in scientific notation.
a.) 532, b.) 4.71
c.) d.) 78,560,000

13. Computing with Scientific Notation
Express each number in scientific notation.
a.) (2 X 104) (4 X 103)
b.) (3.0 X 10-3)2

14. (4.8 X 104) (1.2 X 10-1)

15. Multiplying with Scientific Notation
How much water does the Amazon River discharge into the Atlantic Ocean each year?

16. Dividing with Scientific Notation
In 1867, the United States purchased Alaska from Russia for $7.2 million. The total area of Alaska is about X 108 acres. What was the price per acre?