2. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

3. Review: Scientific notation expresses a number in the form: M x 10 n Any number between 1 and 10 n is an integer

4. + 3.48 x 10 -4 Solution… 0.0237 x 10 -4 3.5037 x 10 -4

5. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION MULTIPLYING AND DIVIDING

6. Rule for Multiplication When multiplying with scientific notation: 1.Multiply the coefficients together. 2.Add the exponents. 3.The base will remain 10.

7. (2 x 10 3 ) (3 x 10 5 ) = 6 x 10 8

8. (4.6x10 8 ) (5.8x10 6 ) =26.68x10 14 Notice: What is wrong with this example? Although the answer is correct, the number is not in scientific notation. To finish the problem, move the decimal one space left and increase the exponent by one. 26.68x10 14 = 2.668x10 15

9. ( (9.2 x 10 5 ) x (2.3 x 10 7 ) = 21.16 x 10 12 = 2.116 x 10 13

10. (3.2 x 10 -5 ) x (1.5 x 10 -3 ) = 4.8 10 -8

11. Rule for Division When dividing with scientific notation 1.Divide the coefficients 2.Subtract the exponents. 3.The base will remain 10.

12. (8 10 6 ) ÷ (2 10 3 ) = 4 x 10 3

13. Please multiply the following numbers. (5.76 x 10 2 ) x (4.55 x 10 -4 ) = (3 x 10 5 ) x (7 x 10 4 ) = (5.63 x 10 8 ) x (2 x 10 0 ) = (4.55 x 10 -14 ) x (3.77 x 10 11 ) = (8.2 x10 -6 ) x (9.4 x 10 -3 ) =

14. Please multiply the following numbers. (5.76 x 10 2 ) x (4.55 x 10 -4 ) = (3 x 10 5 ) x (7 x 10 4 ) = (5.63 x 10 8 ) x (2 x 10 0 ) = (4.55 x 10 -14 ) x (3.77 x 10 11 ) = (8.2 x10 -6 ) x (9.4 x 10 -3 ) = 2.62 x 10 -1 2.1 x 10 10 1.13 x 10 9 7.71 x 10 -8 1.72 x 10 -2

15. 1.(5.76 x 10 2 ) / (4.55 x 10 -4 ) = 2.(3 x 10 5 ) / (7 x 10 4 ) = 3.(5.63 x 10 8 ) / (2) = 4.(8.2 x 10 -6 ) / (9.4 x 10 -3 ) = 5.(4.55 x 10 -14 ) / (3.77 x 10 11 ) = Please divide the following numbers.

16. 1.(5.76 x 10 2 ) / (4.55 x 10 -4 ) = 1.27 x 10 6 2.(3 x 10 5 ) / (7 x 10 4 ) = 4.3 x 10 0 = 4.3 3.(5.63 x 10 8 ) / (2 x 10 0 ) = 2.82 x 10 8 4.(8.2 x 10 -6 ) / (9.4 x 10 -3 ) = 8.7 x 10 -4 5.(4.55 x 10 -14 ) / (3.77 x 10 11 ) = 1.2 x 10 -25 Please divide the following numbers.

17. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION Raising Numbers in Scientific Notation To A Power

18. (5 X 10 4 ) 2 = (5 X 10 4 ) X (5 X 10 4 ) = (5 X 5) X (10 4 X 10 4 ) = (25) X 10 8 = 2.5 X 10 9

19. 1.(3.45 X 10 10 ) 2 2.(4 X 10 -5 ) 2 3.(9.81 X 10 21 ) 2 Try These: 1.(3.45 X 10 10 ) 2 = (3.45 X 3.45) X (10 10 X 10 10 ) = (11.9) X (10 20 ) = 1.19 X 10 21 2.(4 X 10 -5 ) 2 = (4 X 4) X (10 -5 X 10 -5 ) = (16) X (10 -10 ) = 1.6 X 10 -9 3.(9.81 X 10 21 ) 2 = (9.81 X 9.81) X (10 21 X 10 21 ) = (96.24) X (10 42 ) = 9.624 X 10 43 1.19 X 10 21 1.6 X 10 -9 9.624 X 10 43