1. Warm Up: 2-10-14 Simplify the following. Them find the value
Example: 2 2 ∙ 2 3 = 2 5 =32
3 9 ∙ 3 −7
12 − −5
6 10 ∙ 5 −3 5 −3 ∙ 6 8

2. Multiplying by Powers of 10

3. Patterns with Positive Powers of 10
Power of 10
Standard Form
How many 0’s after the 1?
How many times we moved the decimal point?
1.0× 10 0 1
1.0× 10 1
1.0× 10 2
1.0× 10 3
1.0× 10 4

4. Patterns with Positive Powers of 10
Power of 10
Standard Form
How many 0’s after the 1?
How many times we moved the decimal point?
1.0× 10 0 1
1.0× 10 1 10
1.0× 10 2
100 2
1.0× 10 3
1000 3
1.0× 10 4
10000 4

5. Analyzing Positive Powers of 10
What is the connection between the exponent on the 10 and the number of 0’s after the 1? ___________________________________________________________ __________________________________________________
What is the connection between the exponent on the 10 and the number of times we moved the decimal point? ___________________________________________________________ ___________________________________________________
What direction did we move the decimal point? ___________________________________________________________ ___________________________________________________________

6. Analyzing Positive Powers of 10
What is the connection between the exponent on the 10 and the number of 0’s after the 1? The exponent tells how many zeros are after the 1
What is the connection between the exponent on the 10 and the number of times we moved the decimal point? The exponent tells us how many times to move the decimal point
What direction did we move the decimal point? Right

7. Guided Practice
Using the information you just found, write the following in standard form
6.7 × × 10 4
× × 10 2
× × 10 7

8. Guided Practice
Using the information you just found, write the following in standard form
6.7 × = × =61000
× = × =346
× = × =

9. Patterns with Negative Powers of 10
Power of 10
Standard Form
How many 0’s after the decimal point?
How many times we moved the decimal point?
1.0× 10 −5 4
5 to the left
1.0× 10 −4
1.0× 10 −3
1.0× 10 −2
1.0× 10 −1

10. Patterns with Negative Powers of 10
Power of 10
Standard Form
How many 0’s after the decimal point?
How many times we moved the decimal point?
1.0× 10 −5 4
5 to the left
1.0× 10 −4
0.0001 3
1.0× 10 −3
0.001 2
1.0× 10 −2
0.01 1
1.0× 10 −1
0.1

11. Analyzing Patterns with Negative Powers of 10
What is the connection between the exponent on 10 and the number of 0’s after the decimal point? ________________________________________________________ ________________________________________________________
What is the connection between the exponent on 10 and the number of times we move the decimal point? ________________________________________________________ ________________________________________________________
What direction are we moving the decimal when there is a negative exponent on the 10

12. Analyzing Patterns with Negative Powers of 10
What is the connection between the exponent on 10 and the number of 0’s after the decimal point? The number of 0’s is one less than the exponent
What is the connection between the exponent on 10 and the number of times we move the decimal point? The exponent tells us how many times to move the decimal point
What direction are we moving the decimal when there is a negative exponent on the 10? Left

13. Practice
Using the information from the previous slide, write the following in standard form  
× 10 − × 10 −6
× 10 − × 10 −4
× 10 − × 10 −2

14. Practice
Using the information from the previous slide, write the following in standard form  
× 10 −1 = × 10 −6 =
× 10 −7 = × 10 −4 =
× 10 −3 = × 10 −2 =

15. What did we just find?
We just found the standard form for Scientific Notation
Scientific Notation is a way to write Small and Large numbers in a form that makes it easy to calculate and compare numbers that are too large or small to work with.
We write Scientific Notation as a number between 1 and 10 multiplied by a power of 10

16. Writing Numbers in Scientific Notation

17. Writing Really Big Numbers into Scientific Notation
Standard Form
Re-writing into a number between 1 and 10
Number of numbers after the decimal point.
Number of Times we moved the decimal point
Scientific Notation
1,234.0
1.234 3
3 to the left
1.234× 10 3
1,2345
123,456
1,234,567
12,345,678

18. Writing Really Big Numbers into Scientific Notation
Standard Form
Re-writing into a number between 1 and 10
Number of numbers after the decimal point.
Number of Times we moved the decimal point
Scientific Notation
1,234.0
1.234 3
3 to the left
1.234× 10 3
1,2345
1.2345 4
1.2345× 10 4
123,456 5
× 10 5
1,234,567 6
× 10 6
12,345,678 7
× 10 7

19. Analyzing Writing Big Numbers in Scientific Notation
What kind of exponent do we use when writing Big Numbers into Scientific Notation? ______________________________________________________________________________
How do we know what positive number to use for the exponent on the 10 when we write a Big Number in Scientific Notation? ______________________________________________________________________________
What direction do we move the decimal point when writing big numbers in Scientific Notation? ______________________________________________________________________________
Why is the exponent positive when we write big numbers in Scientific Notation? ______________________________________________________________________________
What is the connection between the exponent on the 10 and the number of numbers after the decimal point? ______________________________________________________________________________

20. Analyzing Writing Big Numbers in Scientific Notation
What kind of exponent do we use when writing Big Numbers into Scientific Notation? We use a positive exponent
How do we know what positive number to use for the exponent on the 10 when we write a Big Number in Scientific Notation? We count how many times we move the decimal point
What direction do we move the decimal point when writing big numbers in Scientific Notation? Right
Why is the exponent positive when we write big numbers in Scientific Notation? ______________________________________________________________________________
What is the connection between the exponent on the 10 and the number of numbers after the decimal point? The exponent tells us how many numbers should be after the decimal point

21. Writing in Scientific Notation
Write the following numbers in Scientific Notation
15. 79, ,590
17. 4,733, ,204,000,000

22. Writing in Scientific Notation
Write the following numbers in Scientific Notation
=3.4×
15. 79,700=7.97× ,590
17. 4,733,800= × ,204,000,000

23. Writing Really Small Numbers into Scientific Notation
Standard Form
Re-writing into a number between 1 and 10
Number of Times we moved the decimal point
Scientific Notation
0.12
01.2=1.2
1 to the right
1.2× 10 −1
0.022
0.0032

24. Analyzing Writing Really Small Numbers in Scientific Notation
What kind of exponent for the 10 do we use when writing Small Numbers in Scientific Notation? _____________________________________________________
How do we know what the negative number will be for the exponent on the 10 when writing Small Numbers in Scientific Notation? _______________________________________________________
What direction do we move the decimal point when we write small numbers into Scientific Notation? ______________________________________________________
Why is the exponent negative when we write small numbers in Scientific Notation? __________________________________________________________

25. Analyzing Writing Really Small Numbers in Scientific Notation
What kind of exponent for the 10 do we use when writing Small Numbers in Scientific Notation? Negative
How do we know what the negative number will be for the exponent on the 10 when writing Small Numbers in Scientific Notation? Count how many times we moved the decimal
What direction do we move the decimal point when we write small numbers into Scientific Notation? Right
Why is the exponent negative when we write small numbers in Scientific Notation? _______________________________________________________ ___

26. Practice Write the following numbers in Scientific Notation
=9.16× 10 −
=5.71× 10 −
=1.21× 10 −