8 Powers of 10 and Scientific Notation Notes.notebook
August 25, 2016
review day 8
powers of 10 and scientific notation
Jun 28­9:43 PM
Objective: To be able to use the 10 trick to multiply by powers of 10. To be able to turn any number into scientific notation, and to be able to understand the number being discussed in scientific notation.
Virtue/Skill: Science uses scientific notation when measuring and describing many things, distances or forces that are really big or really small.
Jul 16­10:06 AM
1
8 Powers of 10 and Scientific Notation Notes.notebook
Powers
of
Ten
August 25, 2016
When you multiply by powers of 10, the number gains place value, simply put the decimal moves to the right the number of times there are 0s in the power of 10 number and if there are extra spots they are filled with 0s.
ex. 1 83.924 x 10
ex. 2 83.924 x 100
ex. 3 83.924 x 1000000
When you multiply by a decimal power of 10, you are really dividing by powers of 10, and the number loses place value, simply put the decimal moves to the left the number of times there are 0s in the power of 10 number and if there are extra spots they are filled with 0s.
ex. 1 83.924 x .1
ex. 2 83.924 x .001
ex. 3 83.924 x .000001
Aug 12­12:49 PM
Scientific
Notation
When a really big number or small number need to be discussed, they are rounded to three digits, and the number is turned into a number between 1 and 10 using powers of ten.
ex. 1 7.34 x 1019
ex. 2 83.924 x 1015
ex. 3 83.924 x 10­7
If the exponent is positive move that many places to the right, so the number is bigger
If the exponent is negative move that many places to the left, so the number is smaller.
ex. 1 7.34 x 109
ex. 2 8.92 x 108
ex. 3 2.36 x 10­7
ex. 4 4.58 x 10­11
Aug 12­12:49 PM
2
8 Powers of 10 and Scientific Notation Notes.notebook
Turn a
August 25, 2016
How to turn a number into scientific notation.
# into
Step 1 Rewrite the number with the first three digits and a decimal after the first (so it's between 1 and 10)
Scientific
Step 2 Count how many places you had to move the decimal to get there, make that the exponent.
Notation
Step 3 If the number was big, keep the exponent postive, if the number was small, make the exponent negative
ex. 1 7,392,534,851,234
ex. 2 4,718,634
ex. 3 .0000037268292
ex. 4 .0000000000570398
ex. 2 8.92 x 108
ex. 3 2.36 x 10­7
ex. 4 4.58 x 10­11
Aug 12­12:49 PM
Summary
Objective: To be able to use the 10 trick to multiply by powers of 10. To be able to turn any number into scientific notation, and to be able to understand the number being discussed in scientific notation.
Virtue/Skill: Science uses scientific notation when measuring and describing many things, distances or forces that are really big or really small.
Assignment: Workbooks pg. 58 or Challenge
Jul 16­10:06 AM
3
8 Powers of 10 and Scientific Notation Notes.notebook
August 25, 2016
Exit Questions
1. Put this number in scientific notation: 0.000000048291
2. What does this equal: 30,284.5 x 0.0001
Jul 16­10:05 AM
Answers to pg. 23
1. 7.065
2. 706.09
5. 11.741
6. 1.92
10. 34.853
3. 12.047 7.0.171
11. 10.761
4.$1.66
8. 9.187
9. 5.574
12. 10.37
Answers to pg. 28
14. 0.42
15. 32.13
16. 9.282
17. 0.0156
18. 8.439
19. 0.03294
20. 2.652
21. 0.3213
22. 31.248
23. 0.016
24. 24.96
25. 0.207
26. 3.6
27. 0.00069
28. 6.8016
29. 0.387
30. 0.0124
31. 15.66
32. 0.192
33. 80.04
34. 0.0012
35. 8.12
36. 1.44
37. 9.8 Aug 18­3:53 PM
4
8 Powers of 10 and Scientific Notation Notes.notebook
August 25, 2016
Answers to pg. 32
19. 19
20. 0.06
21. 205
22. 0.68
23. 968
24. 4
25. 87
26. 0.0015
27. 2001
28. 600
29. 1.015
30. 8.5
31. 3
32. 49
33. 651
34. 1550
35. 180
36. 982
37. 36
38. 72.72
39.10.02
40. 22
41. 20
42. 24
43. 0.88
44. 42.1
45. 4.1
Answers to pg. 34
10. 77,000
11. 14,300
12. 150
13. 15
14. 1360
15. 0.184
16. 0.017
17. 0.0008
18. 14,320,000
19. 430
20 0.135
21. 0.55
22. 13,700
23. 43,000
24. 28,100
25. 780
26. 654
27. 0.198
29. 0.15
30. 0.125
31. 1400
32. 0.385
33. 88
34. 1400
35. 1340
36. 1.48 37. 12.3
38. 4326
39. 0.08118
40. 4,800,00
41. 68,200
42. 0.02813
Aug 18­4:09 PM
5