1. The Math of Scientific Notation Chemistry Dr. May

2. Multiplying 40,000,000,000 x 200,000 = (4.0 x 10 10 ) (2.0 x 10 5 ) 8,000,000,000,000,000 8.0 x 10 15

3. Multiplying (4.0 x 10 10 ) (2.0 x 10 5 ) 4.0 x 2.0 = 8.0 10 10 x 10 5 = 10 10 + 5 = 10 15 (4.0 x 10 10 ) (2.0 x 10 5 ) = 8.0 x 10 15

4. Multiplying 40,000,000,000 x 0.000020 = (4.0 x 10 10 ) (2.0 x 10 –5 ) 800,000 = 8.0 x 10 5

5. Multiplying (4.0 x 10 10 ) (2.0 x 10 –5 ) 4.0 x 2.0 = 8.0 10 10 x 10 –5 = 10 10 + (–5) = 10 10 – 5 = 10 5 (4.0 x 10 10 ) (2.0 x 10 –5 ) = 8.0 x 10 5

6. Multiplying 0.00000000040 x 0.000020 = (4.0 x 10 –10 ) (2.0 x 10 –5 ) 0.0000000000000080 = 8.0 x 10 –15

7. Multiplying (4.0 x 10 –10 ) (2.0 x 10 –5 ) 4.0 x 2.0 = 8.0 10 –10 x 10 –5 = 10 –10+(–5) = 10 –10 –5 = 10 –15 (4.0 x 10 –10 ) (2.0 x 10 –5 ) = 8.0 x 10 –15

8. Dividing 4.0 x 10 10 2.0 x 10 5 4.0  2.0 = 2.0 10 10  10 5 = 10 10 – 5 = 10 5 4.0 x 10 10 = 2.0 x 10 5 2.0 x 10 5

9. Dividing 4.0 x 10 10 2.0 x 10 –5 4.0  2.0 = 2.0 10 10  10 –5 = 10 10 – (– 5) = 10 10+5 = 10 15 4.0 x 10 10 = 2.0 x 10 15 2.0 x 10 –5

10. Dividing 4.0 x 10 –10 2.0 x 10 –5 4.0  2.0 = 2.0 10 –10  10 –5 = 10 –10 – (– 5) = 10 –10 + 5 10 –5 4.0 x 10 –10 = 2.0 x 10 –5 2.0 x 10 –5

11. Squaring (3.0 x 10 8 ) 2 (3.0) 2 = 9.0 (10 8 ) 2 = 10 2x8 = 10 16 (3.0 x 10 8 ) 2 = 9.0 x 10 16

12. Square Roots ____________  9.0 x 10 16 _____ _______  9.0 = 3.0  10 16 = 10 16  2 = 10 8 _____________  9.0 x 10 16 = 3.0 x 10 8

13. The End This presentation was created for the benefit of our students by the Science Department at Howard High School of Technology Please send suggestions and comments to rmay@nccvt.k12.de.us