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Warm Up: 2-10-14
• Simplify the following. Them find the valueExample:
Multiplying by Powers of 10
Patterns with Positive Powers of 10Power of 10 Standard Form How many 0’s after the 1? How many times we
moved the decimal point?
1 0 0
Patterns with Positive Powers of 10Power of 10 Standard Form How many 0’s after the 1? How many times we
moved the decimal point?
1 0 0
10 1 1
100 2 2
1000 3 3
10000 4 4
Analyzing Positive Powers of 10
1. What is the connection between the exponent on the 10 and the number of 0’s after the 1? _____________________________________________________________________________________________________________
2. What is the connection between the exponent on the 10 and the number of times we moved the decimal point? ______________________________________________________________________________________________________________
3. What direction did we move the decimal point? ______________________________________________________________________________________________________________________
Analyzing Positive Powers of 10
1. 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
2. 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
3. What direction did we move the decimal point? Right
Guided Practice
• Using the information you just found, write the following in standard form
1. 6.7 × 2. 6.1 ×
3. 1.6 × 4. 3.46 ×
5. 2.91 × 6. 8.651 ×
Guided Practice
• Using the information you just found, write the following in standard form
1. 6.7 × =67 2. 6.1 × =61000
3. 1.6 × =1600 4. 3.46 × =346
5. 2.91 × =291000 6. 8.651 × =86520000
Patterns with Negative Powers of 10Power of 10 Standard Form How many 0’s after the
decimal point?How many times we moved the decimal point?
0.00001 4 5 to the left
Patterns with Negative Powers of 10Power of 10 Standard Form How many 0’s after the
decimal point?How many times we moved the decimal point?
0.00001 4 5 to the left
0.0001 3 4
0.001 2 3
0.01 1 2
0.1 0 1
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
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
Practice
• Using the information from the previous slide, write the following in standard form
7. 3.35 × 8. 7.3 ×
9. 1.49 × 10. 4.0027 ×
11. 5.2277 × 12. 8.50284 ×
Practice
• Using the information from the previous slide, write the following in standard form
7. 3.35 × =0.335 8. 7.3 × =0.0000073
9. 1.49 × =.000000149 10. 4.0027 × =0.00040027
11. 5.2277 × =.0052277 12. 8.50284 × =0.0850284
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
Writing Numbers in Scientific Notation
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
1,2345
123,456
1,234,567
12,345,678
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
1,2345 1.2345 4 4
123,456 1.23456 5 5
1,234,567 1.234567 6 6
12,345,678 1.2345678 7 7
Analyzing Writing Big Numbers in Scientific Notation
1. What kind of exponent do we use when writing Big Numbers into Scientific Notation? ______________________________________________________________________________
2. How do we know what positive number to use for the exponent on the 10 when we write a Big Number in Scientific Notation? ______________________________________________________________________________
3. What direction do we move the decimal point when writing big numbers in Scientific Notation? ______________________________________________________________________________
4. Why is the exponent positive when we write big numbers in Scientific Notation? ______________________________________________________________________________
5. What is the connection between the exponent on the 10 and the number of numbers after the decimal point? ______________________________________________________________________________
Analyzing Writing Big Numbers in Scientific Notation
1. What kind of exponent do we use when writing Big Numbers into Scientific Notation? We use a positive exponent
2. 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
3. What direction do we move the decimal point when writing big numbers in Scientific Notation? Right
4. Why is the exponent positive when we write big numbers in Scientific Notation? ______________________________________________________________________________
5. 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
Writing in Scientific Notation
• Write the following numbers in Scientific Notation13. 34 14. 273
15. 79,700 16. 6,590
17. 4,733,800 18. 2,204,000,000
Writing in Scientific Notation
• Write the following numbers in Scientific Notation13. 34 = 14. 273
15. 79,700= 16. 6,590
17. 4,733,800= 18. 2,204,000,000
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
0.022
0.0032
0.00042
0.000052
Analyzing Writing Really Small Numbers in Scientific Notation1. What kind of exponent for the 10 do we use when writing Small Numbers in
Scientific Notation? _____________________________________________________
2. How do we know what the negative number will be for the exponent on the 10 when writing Small Numbers in Scientific Notation? _______________________________________________________
3. What direction do we move the decimal point when we write small numbers into Scientific Notation? ______________________________________________________
4. Why is the exponent negative when we write small numbers in Scientific Notation? __________________________________________________________
Analyzing Writing Really Small Numbers in Scientific Notation1. What kind of exponent for the 10 do we use when writing Small
Numbers in Scientific Notation? Negative2. 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
3. What direction do we move the decimal point when we write small numbers into Scientific Notation? Right
4. Why is the exponent negative when we write small numbers in Scientific Notation? __________________________________________________________
Practice
• Write the following numbers in Scientific Notation19. 0.00916 = 20. 0.29
21. 0.00000571= 22. 0.0008331
23. 0.0121= 24. 0.00000018