1. Powers of Ten

2. Learning Target: I can explain the relationship between a digit and how it is both ten times the number on its right and ten times less than the number on the left.
Powers of Ten Day 1

3. Tenths, hundredths, and thousandths
You may know that
Place
Value
One tenth
One hundredth
One thousandth

4. Tenths, hundredths, and thousandths
You should also know
Place
Value
Power of Ten
One tenth
1 ÷ 10
One hundredth
1 ÷ 100 or 1 ÷ 10 x 10
One thousandth
1 ÷ 1000 or 1 ÷ 10 x 10 x 10

5. Powers of Ten
As numbers get larger than 1, they are being multiplied by 10. As numbers get smaller than 1, they are being divided by 10.
When you multiply 3 x 10, the answer is 30. You could also figure this out by moving the decimal to the right, shifting the numbers to the left.
3 can also be seen as 3.0
3.0 x 10 = 30.0

6. 55 = 5 is ten times larger than 5
Powers of Ten
When looking at a specific digit, it will always be ten times larger than the number to its left
55 = 5 is ten times larger than 5

7. Powers of Ten

8. 5 5 5 5 5 5
So that means

9. Turn and Talk A B C In the number 555.555
In how much larger is the light blue 5 than the red 5? B C
In how much smaller is the light blue 5 than the red 5?
In the number
Each 5 on the left is 10 times larger than the one on the right
Each 5 on the right is 10 times smaller than the one on the left.

10. Turn and Talk A B C In the number 555.555
In how much larger is the light blue 5 than the red 5? Ten times larger B
In how much larger is the light blue 5 than the red 5? One hundred times larger C
In how much smaller is the red 5 than the light blue 5 ? Ten times smaller
In the number
Each 5 on the left is 10 times larger than the one on the right
Each 5 on the right is 10 times smaller than the one on the left.

11. How is the value of the digit “2” in the number 15
How is the value of the digit “2” in the number different from the value of the digit “2” in the number 12.54?
15.42
12.54

12. How is the value of the digit “2” in the number 15
How is the value of the digit “2” in the number different from the value of the digit “2” in the number 12.54?
15.42
12.54
You could look at it as money, $0.02
You could look at it as money, $2.00

13. How is the value of the digit “2” in the number 15
How is the value of the digit “2” in the number different from the value of the digit “2” in the number 12.54?
15.42
12.54
You could look at it as money, $0.02
You could look at it as money, $2.00

14. How is the value of the digit “2” in the number 15
How is the value of the digit “2” in the number different from the value of the digit “2” in the number 12.54?
15.42
12.54
You could look at it as money, $0.02
The 2 in is
100 times smaller
than the the 2 in 12.54
You could look at it as money, $2.00
The 2 in is 100 times larger
than 0.02

15. Turn and Talk
How is the value of the digit 1 in 1,000 different from the digit 1 in 0.001? 1,
.001

16. Turn and Talk

17. Additional Examples
What is the difference between the 3 in and 3.4?

18. Try these on your own 3 .
x 10
X 10

19. What is the difference between the 3 in 0.034 and 3.4?
The 3 in 3.4 is in the ones place. The 3 in is in the hundredths place.
3.0
.03

20. Review of Exponents and Scientific Notation
What is the difference between the 3 in and 3.4?
The 3 in 3.4 is in the ones place. The 3 in is in the hundredths place.
3.0
.03
If you divide 3.0 by 100, you will get 0.03.

21. Try in on your own then check with a shoulder buddy
Look at the numbers 51.4 and Explain what would happen to the value of the digit 5 if you moved it from the tens place to the tenths place?
51.4
14.5

22. Try in on your own then check with a shoulder buddy

23. Dividing by Powers of Ten
Look at the numbers 14.5 and 51.4
Look at the numbers 51.4 and Explain what would happen to the value of the digit 4 if you moved it from the tenths place to the ones place?
51.4
14.5
The 4 in the ones place is ten times larger than the 4 in the tenths place (0.4). The value of the 4 would become ten times larger.

24. Review of Exponents and Scientific Notation
What is the difference between the 6 in 6, and 6.92?

25. Review of Exponents and Scientific Notation

26. Try on your own, check with a shoulder buddy
Look at the numbers and
Explain what happens to the value of 3 as you move it from the tens place to the hundreds place .
Explain what happens to the value of the digit 6 as you move it from the thousandths place to the tens place.

27. Try on your own, check with a shoulder buddy

28. Did you achieve your Learning Target
Did you achieve your Learning Target? I can explain the relationship between a digit and how it is both ten times the number on its right and ten times less than the number on the left.

29. Powers of Ten
Day 2

30. I can multiply a digit by powers of ten.
Learning Target: I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left.
I can multiply a digit by powers of ten.

31. Introduction to Powers of Ten forms
"Powers of 10" is a very useful way of writing down large or small numbers.
Instead of having lots of zeros, you show how many powers of 10 will make that many zeros
Example: 5,000 = 5 × 1,000 = 5 × 103
Scientists and Engineers (who often use very big or very small numbers) like to write numbers this way.
Example: The Mass of the Sun
The Sun has a Mass of × 1030 kg.
It would be too hard to write ,988,000,000,000,000,000,000,000,000,000 kg
Cosmic Voyage Video
Start at 6:43 and end at 11:40

32. Expanded Form and Powers of Ten
The number 10,957,107 in expanded form shows the relationship between powers of ten and the way we can think about numbers in another way.
10,957,107 =
1 x 10,000,000
9 x 100,000
5 x 10,000
7 x 1,000
1 x 100
_+__________7 x 1
10,957,107

33. Multiplying by 10’s Place Value is based on powers of 10: Place Value
Number of 10’s Multiplied
1 Billion
1,000,000,000
10x10x10x10x10x10x10x10x10
100 Million
100,000,000
10x10x10x10x10x10x10x10
10 Million
10,000,000
10x10x10x10x10x10x10
1 Million
1,000,000
10x10x10x10x10x10
100 Thousand
100,000
10x10x10x10x10
10 Thousand
10,000
10x10x10x10
1 Thousand
1,000
10x10x10
1 Hundred
100
10x10
1 Ten 10 1

34. Lets use exponents to show how numbers shift when multiplied by tens.
4 x 103 = 4 x 10 x 10 x 10 =
64 x 102 = 64 x 10 x 10 =
8.3 x 103 = 8.3 x 10 x 10 x 10 =
0.4 x 104 = 0.4 x 10 x 10 x10 x 10 =
102 = 10 x 10
105 = 10 x 10 x 10 x 10 x 10

35. You can use exponents to show how numbers shift.
4 x 103 = 4 x 10 x 10 x 10 = 4,000
64 x 102 = 64 x 10 x 10 = 6,400
8.3 x 103 = 8.3 x 10 x 10 x 10 = 8,300
0.4 x 104 = 0.4 x 10 x 10 x10 x 10 =
4,000
102 = 10 x 10
105 = 10 x 10 x 10 x 10 x 10

36. Try it on your own then check with a peer:
EXPONENTS
Try it on your own then check with a peer:
3 x 102 = 3 x 10 x 10 =
72 x 103 = 72 x 10 x 10 x 10 =
1.4 x 103 = 1.4 x 10 x 10 x 10 =
0.5 x 104 = 0.5 x 10 x 10 x10 x 10 =
102 = 10 x 10
105 = 10 x 10 x 10 x 10 x 10

37. Try it on your own then check with a peer:
EXPONENTS
Try it on your own then check with a peer:
3 x 102 = 3 x 100 = 300
72 x 103 = 72 x 1000 =72,000
1.4 x 103 = 1.4 x 1000 = 1,400
0.5 x 104 = 0.5 x 10,000 = 5,000
102 = 10 x 10
105 = 10 x 10 x 10 x 10 x 10

38. Try it on your own then check with a peer:
EXPONENTS
Try it on your own then check with a peer:
72 x 103 = 72 x 10 x 10 x 10 =
You may see it this way, but…
1.4 x 103 = 1.4 x 10 x 10 x 10 =
This is the proper way to
write a decimal with powers of
ten.
102 = 10 x 10
105 = 10 x 10 x 10 x 10 x 10

39. DECIMALS AND EXPONENTS
Scientific Notation
10,000 = 10 x 10 x 10 x 10 =
100,000,000 =10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 =
500,000 =5 x 10 x 10 x 10 x 10 x 10=
1,500 = 1.5 x 10 x 10 x 10 = 1.5 x 103
When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out.
304,000 = 3.04 x 105
1,300,000 = 1.3 x 106
23,502,000 = x 107

40. DECIMALS AND EXPONENTS
Scientific Notation
10,000 = 10 x 10 x 10 x 10 = 104
100,000,000 =10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 =
108
500,000 =5 x 10 x 10 x 10 x 10 x 10=
5 x 105
1,500 = 1.5 x 10 x 10 x 10 = 1.5 x 103
When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out.
304,000 = 3.04 x 105
1,300,000 = 1.3 x 106
23,502,000 = x 107

41. DECIMALS AND EXPONENTS
Work on your own and check with a shoulder buddy:
100 = 10 x 10 =
1,000,000 =10 x 10 x 10 x 10 x 10 x 10 =
2,000,000= 2 x 10 x 10 x 10 x 10 x 10 x 10 =
320,000 = 3.2 x 10 x 10 x 10 x 10 x 10 =
When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out.
304,000 = 3.04 x 105
1,300,000 = 1.3 x 106
23,502,000 = x 107

42. DECIMALS AND EXPONENTS
Work on your own and check with a shoulder buddy:
100 = 10 x 10 = 102
1,000,000 =10 x 10 x 10 x 10 x 10 x 10 = 106
2,000,000= 2 x 10 x 10 x 10 x 10 x 10 x 10 =
2 x 106
320,000 = 3.2 x 10 x 10 x 10 x 10 x 10 =
3.2 x 105
When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out.
304,000 = 3.04 x 105
1,300,000 = 1.3 x 106
23,502,000 = x 107

43. I can multiply a digit by powers of ten.
Did you achieve your Learning Targets? I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left.
I can multiply a digit by powers of ten.

44. EXIT TICKET 555.555 What is the difference in the 5 and the 5?
What is the relationship with a digit, and the digit to its left and right? (Ex. 3.33)
What is the value of any number once you multiply it by 103 ?
What is the value of 2.5 x 103 ?
Write the 100,000 as an exponent (also known as scientific notation).

45. Powers of Ten
Day 3

46. EXIT TICKET

47. I can multiply and divide a digit by powers of ten.
Learning Target: I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left.
I can multiply and divide a digit by powers of ten.

48. Review of multiplying by 10’s
Remember that Place Value is based on powers of 10:
Place
Value
Number of 10’s Multiplied
1 Billion
1,000,000,000
10x10x10x10x10x10x10x10x10
100 Million
100,000,000
10x10x10x10x10x10x10x10
10 Million
10,000,000
10x10x10x10x10x10x10
1 Million
1,000,000
10x10x10x10x10x10
100 Thousand
100,000
10x10x10x10x10
10 Thousand
10,000
10x10x10x10
1 Thousand
1,000
10x10x10
1 Hundred
100
10x10
1 Ten 10 1

49. Tenths, hundredths, and thousandths
You should also know
Place
Value
Power of Ten
One tenth
1 ÷ 10
One hundredth
1 ÷ 100 or 1 ÷ 10 x 10
One thousandth
1 ÷ 1000 or 1 ÷ 10 x 10 x 10
When you multiply by powers of ten, the decimal moves right.
Ex. 47 x 100 = or 47.0 x 100 = 4,700.0
5.4 x 103= 5.4 x 103 = 5,400 or 5,400.0

50. Tenths, hundredths, and thousandths
You should also know
Place
Value
Power of Ten
One tenth
1 ÷ 10
One hundredth
1 ÷ 100 or 1 ÷ 10 x 10
One thousandth
1 ÷ 1000 or 1 ÷ 10 x 10 x 10
Multiplying by 0.1 and dividing by ten have the same results.
Multiplying by 0.01 and dividing by 100 have the same result.
Multiplying by and dividing by _____ have the same result.

51. Tenths, hundredths, and thousandths
You should also know
Place
Value
Power of Ten
One tenth
1 ÷ 10
One hundredth
1 ÷ 100 or 1 ÷ 10 x 10
One thousandth
1 ÷ 1000 or 1 ÷ 10 x 10 x 10
Multiplying by 0.1 and dividing by ten have the same results.
Multiplying by 0.01 and dividing by 100 have the same result.
Multiplying by and dividing by 1,000 have the same result.

52. Dividing with Powers of Ten

53. You can use exponents to show how numbers shift when dividing.
7 x 10-3 = 7 x 0.1 x 0.1 x 0.1 =
22 x 10-2 = 22 ÷ 10 ÷ 10 =
8.3 x 10-3 = 8.3 x 0.1 x 0.1 x 0.1 =
0.4 x 10-4 = 0.4 ÷10 ÷10 ÷10 ÷10 =
10-2 = 0.1 x 0.1= 0.01
10-2 = 1 ÷ 10 ÷ 10 = 0.01
10-5 = 0.1 x 0.1 x 0.1 x 0.1 x 0.1=
10-5 = ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 =

54. EXPONENTS
You can use exponents to show how numbers shift when dividing.
7 x 10-3 = 7 x 0.1 x 0.1 x 0.1 = 0.007
22 x 10-2 = 22 ÷ 10 ÷ 10 = 0.22
8.3 x 10-3 = 8.3 x 0.1 x 0.1 x 0.1 =
0.4 x 10-4 = 0.4 ÷10 ÷10 ÷10 ÷10 =
0.0004
10-2 = 0.1 x 0.1= 0.01
10-2 = 1 ÷ 10 ÷ 10 = 0.01
10-5 = 0.1 x 0.1 x 0.1 x 0.1 x 0.1=
10-5 = ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 =

55. Try it on your own, check with a Shoulder Buddy
EXPONENTS
Try it on your own, check with a Shoulder Buddy
4 x 10-3 = 4 x 0.1 x 0.1 x 0.1 =
64 x 10-2 = 64 ÷10 ÷10 =
6.1 x 10-3 = 6.1 x 0.1 x 0.1 x 0.1 =
0.3 x 10-4 = 0.3 ÷10 ÷10 ÷10 ÷10 =
10-2 = 0.1 x 0.1= 0.01
10-5 = 0.1 x 0.1 x 0.1 x 0.1 x 0.1=

56. EXPONENTS Try it on your own, check with a Shoulder Buddy
4 x 10-3 = 4 x 0.1 x 0.1 x 0.1 = 0.004
64 x 10-2 = 64 ÷10 ÷10 =0.64
6.1 x 10-3 = 6.1 x 0.1 x 0.1 x 0.1 =
0.0061
0.3 x 10-4 = 0.3 x 0.3 ÷10 ÷10 ÷10 ÷10 =
0.0003
10-2 = 0.1 x 0.1= 0.01
10-5 = 0.1 x 0.1 x 0.1 x 0.1 x 0.1=

57. DECIMALS AND EXPONENTS
When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out.
0.051 = 5.1 x 10-2
0.1300= 1.3 x 10-1
= x 10-1
= 1.5 x 10-5
= 4.11 x 10-3

58. DECIMALS AND EXPONENTS
When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out.
0.051 = 5.1 x 10-2
0.1300= 1.3 x 10-1
= x 10-1
= 1.5 x 10-5
= 4.11 x 10-3

59. DECIMALS AND EXPONENTS
Scientific Notation
= 2 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 = = =
When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out.
0.051 = 5.1 x 10-2
0.1300= 1.3 x 10-1
= x 10-1
= 1.5 x 10-5
= 4.11 x 10-3

60. DECIMALS AND EXPONENTS
Scientific Notation
= 2 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 = 2 x 10-5
= 5 x 10-5
= x 10-3
= 8.9 x 10-7
When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out.
0.051 = 5.1 x 10-2
0.1300= 1.3 x 10-1
= x 10-1
= 1.5 x 10-5
= 4.11 x 10-3

61. DECIMALS AND EXPONENTS
Scientific Notation
= 2 ÷10 ÷10 ÷10 ÷10 ÷10 =
2 ÷10-5
= 5 ÷10-5
Try these one your own: = =
At times you’ll see exponents this way:
4,500 ÷ 103 = 4.5
290,400,000 ÷ 105 =
Dividing by powers or ten is the same as multiplying by negative powers of ten.

62. DECIMALS AND EXPONENTS
Scientific Notation
= 2 ÷10 ÷10 ÷10 ÷10 =
2 ÷104
= 5 ÷105
= 4.44 ÷ 103
=8.9 ÷ 107
At times you’ll see exponents this way:
4,500 ÷ 103 = 4.5
290,400,000 ÷ 105 =
Dividing by powers or ten is the same as multiplying by negative powers of ten.

63. I can multiply and divide a digit by powers of ten.
Did you achieve your Learning Target? I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left.
I can multiply and divide a digit by powers of ten.

64. EXIT TICKET 555.555 What is the difference in the 5 and the 5?
What is the value of any number once you multiply it by 10-3 ?
What is the value of 1.05 x 10-3 ?
What is 3.04 ÷ 103 ?
Write the as an exponent (also known as scientific notation).

65. Powers of Ten
Day 4

66. I can multiply and divide a digit by powers of ten.
Learning Target: I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left.
I can multiply and divide a digit by powers of ten.

67. REVIEW YESTERDAYS EXIT TICKET

68. Practice Powers of Ten What is 100.4 x 104 ? What is 5.567 x 102 ?

69. Powers of Ten
What is x 104 ? 1,004,000
What is x 102 ?
What is 6.6 x 10-2 ?
What is 372 ÷ 105 ?

70. 8 thousandths
Practice Powers of Ten
Which value is ten times the value of the digit 7 in ?
7 tens
7 ones
7 tenths
7 hundredths

71. Practice Powers of Ten The value of 7 in 509.171 = 0.07
8 thousandths
Practice Powers of Ten
Which value is ten times the value of the digit 7 in ?
7 tens
7 ones
7 tenths
7 hundredths
The value of 7 in = 0.07
0.07 x 10 = 0.7, which is 7 tenths

72. Powers of Ten If 1,097 x 10n = 10,970, what is the value of n?
n = stands for an “unknown” number.
What could be the exponent that would make this equation true?

73. Powers of Ten If 1,097 x 10n = 10,970, what is the value of n?
n = stands for an “unknown” number.
What could be the exponent that would make this equation true?
1,097 is ten times smaller than 10,970. The opposite operation, of dividing by ten is multiplying by ten so
1,097 x 10n = 10,970, n = 1

74. Try on you own, then check with a shoulder buddy
If 1,097 x 10n = 109,700,000 what is the value of n?
If 3.3 x 10n = 3,300 what is the value of n?
If 3.3 x 10n = 0.033, what is the value of n?
If 64 ÷ 10n = , what is the value of n?

75. Try on you own, then check with a shoulder buddy
If 1,097 x 10n = 109,700,000 what is the value of n?
n = 5 because 1,097 x 105 = 109,700,000
If 3.3 x 10n = 3,300 what is the value of n?
n = 3 because 3.3 x 103 = 3,300
If 3.3 x 10n = 0.033, what is the value of n?
n = -2 because 3.3 x 10-2 = 0.033
If 64 ÷ 10n = , what is the value of n?
n = 4 because 64 ÷ 104 =

76. More Practice with Powers of Ten
Annie had the answer showing on her calculator after dividing a number by ten. What was the original number? Explain how you know.

77. Dividing with Powers of Ten

78. Powers of Ten
Explain what happens to the value of the digits when multiplied and divided by a power of 10 using the two examples below.
2,500 ÷ x 103

79. Powers of Ten

80. I can multiply and divide a digit by powers of ten.
Did you achieve your Learning Target? I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left.
I can multiply and divide a digit by powers of ten.

81. I can multiply and divide a digit by powers of ten.
Any questions? Did you achieve your Learning Target? I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left.
I can multiply and divide a digit by powers of ten.

82. Great, now please clear off your desk
You will need a sheet of notebook paper and a sharpened
pencil for your 1st quick quiz common assessment in math!