1. Multiplying and Dividing in Scientific Notation

2. Multiplying Numbers in Scientific Notation Multiply the decimal numbers together. Add the exponents to get the power of 10. Sometimes, you might have to adjust it so that the answer is in proper scientific notation. General formula: (a X 10 x ) (b X 10 y ) = (ab) X 10 x+y

3. Example 1 3.42 X 10 5 4.67 X 10 9 Multiply decimals: 3.42 X 4.67 = 15.97 Add Exponents: 10 5 x 10 9 =10 5+9 = 10 14 Preliminary Answer: 15.97 X 10 14 Now, Rewrite in Scientific Notation if needed. Final Answer: 1.597 X 10 15

4. Example 2 (2.93 X 10 -2 ) (8.3 X 10 -5 ) (2.93 X 8.3)(10 -2 x 10 -5 ) 24.319 X 10 -7 Final Answer: 2.43 X 10 -6 End of X

5. Dividing Numbers in Scientific Notation Divide the decimal numbers. Then subtract the exponents General formula:

6. Example 1 Given: 8 x 10 -3 2 x 10 -2 Divide decimals: 8÷2 = 4 Subtract exponents: (-3)-(-2)= -1 Final Answer: 4 x 10 -1

7. Example 2 Given: 3.45 X 10 2 1.23 X 10 -5 (3.45 ÷ 1.23)(10 2 ÷ 10 -5 )= 2.81 X 10 7

8. Question 1 Write these 2 numbers in scientific notation: 0.000467 32000000 Question 2 Express 5.43 x 10 -3 in standard form Question 3 (4.5 x 10 -14 ) x (5.2 x 10 3 ) = ? Question 4 (6.1 x 10 5 )/(1.2 x 10 -3 ) = ? Question 5 (3.74 x 10 -3 ) 4 = ? Review/Extended Questions