1. Scientific Notation Init 8/24/2011 by Daniel R. Barnes
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2. MATH PROBLEM:
If the Chicxulub Sisters Copper Mine produces 670,000,000,000,000 tons of copper ore per year
and a Xibalba-class cargo ship can haul
30,800,000 tons of copper ore,
how many shiploads of copper ore does the mine produce each year?
Seriously, you want us to divide 30,800,000 into 670,000,000,000,000? LONG DIVISION?
30,800,000 ) 670,000,000,000,000
ayfkm?

3. SWBAT . . .
. . . convert numbers between regular format and scientific notation.

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

5. SIMPLE POWERS of TEN 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1000
105 = 10 x 10 x 10 x 10 x 10 = 100,000
101 = 10 = 10

6. SIMPLE POWERS of TEN 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1000
105 = 10 x 10 x 10 x 10 x 10 = 100,000
101 = 10 = 10

7. NEGATIVE POWERS of TEN 1 1 10-1 = = = 0.1 101 10 1 1 1 10-2 = = =
= 0.01
102
10 x 10
100 1 1 1
10-3 = = =
= 0.001
103
10 x 10 x10
1000
10-4 1 1 1 = = = =
104
10 x 10 x 10 x 10
10,000

8. NEGATIVE POWERS of TEN 1 1 10-1 = = = 0.1 101 10 1 1 1 10-2 = = =
= 0.01
102
10 x 10
100 1 1 1
10-3 = = =
= 0.001
103
10 x 10 x10
1000
10-4 1 1 1 = = = =
104
10 x 10 x 10 x 10
10,000

9. TEN to the ZERO
103 = 1,000
102 = 100
101 = 10
100 = 1
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
Multiplying zero tens by each other sounds like one hand clapping, but seeing 100 placed in this sequence makes it obvious that it’s the only possible missing piece in the pattern.

10. TEN to the ZERO
103 = 1,000
102 = 100
101 = 10
100 = 1
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
Multiplying zero tens by each other sounds like one hand clapping, but seeing 100 placed in this sequence makes it obvious that it’s the only possible missing piece in the pattern.

11. Exponential
form
English word
Decimal
number
Fractional
form
1,000,000
106
one million
1,000,000 1
1,000
103
one thousand
1,000 1
One
one-hundredth 1 1
10-2
0.01 =
100
102
One
ten-thousandth 1
10-4
0.0001
10,000 1
100
one 1 1

12. Exponential
form
English word
Decimal
number
Fractional
form
1,000,000
106
one million
1,000,000 1
1,000
103
one thousand
1,000 1
One
one-hundredth 1 1
10-2
0.01 =
100
102
One
ten-thousandth 1
10-4
0.0001
10,000 1
100
one 1 1

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

14. Exponential
form
English word
Decimal
number
Fractional
form 50
fifty 50
5 x 101 1
Twenty
million
20,000,000
20,000,000
2 x 107 1
four
one-thousandths 4
0.004
4 x 10-3
1000
Seven
trillion
7 x 1012
7,000,000,000,000
Three
One hundred
millionths 3
3 x 10-8
100,000,000

15. Exponential
form
English word
Decimal
number
Fractional
form 50
fifty 50
5 x 101 1
Twenty
million
20,000,000
20,000,000
2 x 107 1
four
one-thousandths 4
0.004
4 x 10-3
1000
Seven
trillion
7 x 1012
7,000,000,000,000
Three
One hundred
millionths 3
3 x 10-8
100,000,000

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

17. 2015 . Convert “2015” to scientific notation
There’s a decimal point hiding in this number. Where is it?
To where do we move the decimal point?
2015 .
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.

18. . 2.015 2015 Convert “2015” to scientific notation
To where to we move the decimal point? .
2.015
2015
In this case, three spaces to the left.

19. 2.015 x 103 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.
2.015
x 103
To bring it back up to being about two thousand again, we need to multiply it by the right power of ten . . .

20. Convert “2015” to scientific notation
2015 =
2.015
x 103

21. Let’s practice with some more numbers.

22. Practice Question #1
465 =
4.65
x 102

23. Practice Question #2
30.7 =
3.07
x 101

24. Practice Question #3
400,000 = 4
x 105

25. Practice Question #4 =
x 101

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

27. Practice Question #6 =
7.67
x 10-3

28. Practice Question #7 =
6.1
x 10-7

29. Practice Question #8
80,000,000,000 = 8
x 1010

30. Practice Question #9 =
9.1123
x 10-8

31. Practice Question #10 =
x 10-3

32. Practice Question #11
229,100,000 =
2.291
x 108

33. Practice Question #12 =
7.212
x 10-7

34. Practice Question #13
39,700,000 =
3.97
x 107

35. That’s great, but, sometimes, you have a number that’s almost
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?

36. Practice Question #14
56.2 x 1027 =
5.62
x 1028

37. Practice Question #15
x 1013 =
9.304
x 1011

38. Practice Question #16
406.7 x 10-7 =
4.067
x 10-5

39. Practice Question #16
x =
3.93
x 10-27