1. Objective 1.To write very large or very small numbers in standard form, in scientific notation, and vice versa. To compare and order numbers in scientific notation Designed by Skip Tyler, Varina High School

2. How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

3. Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer

4. Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

5. 2. 10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 10 23

6. 1) Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10 -8

7. Why does a Negative Exponent give us a small number? 10,000 = 10 x 10 x 10 x 10 = 10 4 1,000 = 10 x 10 x 10 = 10 3 100 = 10 x 10 = 10 2 10 = 10 1 1 = 10 0 Do you see a pattern?

8. Sooooo = 10 -1 = = 10 -2 = = 10 -3 = = 10 -4

9. Write 28750.9 in scientific notation. 1. 2.87509 x 10 -5 2. 2.87509 x 10 -4 3. 2.87509 x 10 4 4. 2.87509 x 10 5

10. 2) Express 1.8 x 10 -4 in decimal notation. 0.00018 3) Express 4.58 x 10 6 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done with the button. 4.58 x 10 6 is typed 4.58 6

11. 4) Use a calculator to evaluate: 4.5 x 10 -5 1.6 x 10 -2 Type 4.5 -5 1.6 -2 You must include parentheses if you don’t use those buttons!! (4.5 x 10 -5) (1.6 x 10 -2) 0.0028125 Write in scientific notation. 2.8125 x 10 -3

12. 5) Use a calculator to evaluate: 7.2 x 10 -9 1.2 x 10 2 On the calculator, the answer is: 6.E -11 The answer in scientific notation is 6 x 10 -11 The answer in decimal notation is 0.00000000006

13. 6) Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is 1386. The answer in decimal notation is 1386 The answer in scientific notation is 1.386 x 10 3

14. 7) Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is: 8.28 E +10 The answer in scientific notation is 8.28 x 10 10 The answer in decimal notation is 82,800,000,000

15. Write (2.8 x 10 3 )(5.1 x 10 -7 ) in scientific notation. 1. 14.28 x 10 -4 2. 1.428 x 10 -3 3. 14.28 x 10 10 4. 1.428 x 10 11

16. Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) 234.6 x 10 9 2.346 x 10 11 9) 0.0642 x 10 4 on calculator: 642 6.42 x 10 2

17. Write 531.42 x 10 5 in scientific notation. 1..53142 x 10 2 2. 5.3142 x 10 3 3. 53.142 x 10 4 4. 531.42 x 10 5 5. 53.142 x 10 6 6. 5.3142 x 10 7 7..53142 x 10 8

18. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION MULTIPLYING AND DIVIDING

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

20. (2 x 10 3 ) (3 x 10 5 ) = 6 x 10 8

21. (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

22. ( (9.2 x 10 5 ) x (2.3 x 10 7 ) = 21.16 x 10 12 = 2.116 x 10 13

23. (3.2 x 10 -5 ) x (1.5 x 10 -3 ) = 4.8 10 -8

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

25. (8 10 6 ) ÷ (2 10 3 ) = 4 x 10 3

26. 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 ) =

27. 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

28. 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.

29. 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.

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

31. (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

32. 1.(3.45 X 10 10 ) 2 (4 X 10 -5 ) 2 (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 3.(4 X 10 -5 ) 2 = (4 X 4) X (10 -5 X 10 -5 ) = (16) X (10 -10 ) = 1.6 X 10 - 9 (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

33. 9.54x10 7 miles 1.86x10 7 miles per second Scientific Notation Makes These Numbers Easy