1. Init 8/24/2011 by Daniel R. Barnes WARNING: This presentation includes images and other content taken from the world wide web without permission of the owners of that content. Do not copy or distribute this presentation. Its very existence may be illegal.

2. ... convert numbers between regular format and scientific notation.

3. First, we must make sure we’ve learned about powers of ten.

4. 10 2 = 10 x 10 = 100 10 3 = 10 x 10 x 10 = 1000 10 5 = 10 x 10 x 10 x 10 x 10 = 100,000 10 1 = 10 = 10 SIMPLE POWERS of TEN

5. 10 -1 NEGATIVE POWERS of TEN 1 = 0.1 = 10 1 = 1 10 10 -2 1 = 0.01 = 10 2 = 1 10 x 10 = 1 100 10 -3 1 = 0.001 = 10 3 = 1 10 x 10 x10 = 1 1000 10 -4 1 = 0.0001 = 10 4 = 1 10 x 10 x 10 x 10 = 1 10,000

6. 10 3 = 1,000 TEN to the ZERO 10 2 = 100 10 1 = 10 10 -1 = 0.1 10 -2 = 0.01 10 -3 = 0.001 10 0 = 1

7. 100 one million1,000,000 Exponential form English word Decimal number Fractional form 10 6 1,000,000 1 one thousand1,00010 3 1,000 1 One one-hundredth 0.0110 -2 1 One ten-thousandth 0.000110 -4 1 10,000 one 110 0 1 1 = 10 2 1

8. Okay. Now Let’s throw in a multiplier.

9. 100,000,000 four one-thousandths 0.0004 4 1000 fifty50 Exponential form English word Decimal number Fractional form 5 x 10 1 50 1 Twenty million 20,000,000 2 x 10 7 20,000,000 1 4 x 10 -3 Seven trillion 7,000,000,000,000 7 x 10 12 Three One hundred millionths 0.00000003 3 x 10 -8 3

10. Alright. Now we can try converting a number to scientific notation.

11. Convert “2015” to scientific notation 2015. There’s a decimal point hiding in this number. Where is it? The first step in converting a number to scientific notation is to move the decimal until there’s one digit in front of it and however many digits are left behind it. To where do we move the decimal point?

12. Convert “2015” to scientific notation 2015. In this case, three spaces to the left. To where to we move the decimal point? 2.015

13. Convert “2015” to scientific notation It looks like we just turned two thousand into two. That’s not right. That’s not what we’re trying to do. To bring it back up to being about two thousand again, we need to multiply it by the right power of ten... x 10 3

14. 2.015 Convert “2015” to scientific notation x 10 3 2015 =

15. Let’s practice with some more numbers.

16. 4.65 x 10 2 465 = Practice Question #1

17. 3.07 x 10 1 30.7 = Practice Question #2

18. 4 x 10 5 400,000 = Practice Question #3

19. 1.31712 x 10 1 13.1712 = Practice Question #4

20. 3.2 x 10 -1 0.32 = Practice Question #5

21. 7.67 x 10 -3 0.00767 = Practice Question #6

22. 6.1 x 10 -7 0.00000061 = Practice Question #7

23. 8 x 10 10 80,000,000,000 = Practice Question #8

24. 9.1123 x 10 -8 0.000000091123 = Practice Question #9

25. 9.630041 x 10 -3 0.009630041 = Practice Question #10

26. 2.291 x 10 8 229,100,000 = Practice Question #11

27. 7.212 x 10 -7 0.0000007212 = Practice Question #12

28. 39.7 x 10 7 39,700,000 = Practice Question #13

29. Okay. That’s great, but, sometimes, you have a number that’s almost in scientific notation, but not quite. What do you do? WHAT DO YOU DO?