Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100 Bellwork Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100 4. 0.003  100 5. 104 6. 10–4 7. 230 123,000 0.123 0.3 0.00003 10,000 0.0001 1

Powers of Ten and Scientific Notation

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

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.

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.

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. 0.000001 10,000 1,000,000,000

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

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

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

Rewriting in Decimal Form Rewrite in decimal form: a.) 3.427 X 103 b.) 5.6 X 1010 c.) 6.5 X 10-1 d.) 2.31 X 10-5

Rewriting in Scientific Notation Rewrite in scientific notation. a.) 532, 236 b.) 4.71 c.) 0.00000849 d.) 78,560,000

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

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

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

Dividing with Scientific Notation In 1867, the United States purchased Alaska from Russia for $7.2 million. The total area of Alaska is about 3.78 X 108 acres. What was the price per acre?