1. Scientific Notation SLIDE SHOW INSTRUCTIONS
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Copyright © 2011 Lynda Greene Aguirre

2. Table of Contents Concepts & Definitions
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Concepts & Definitions
Change Scientific to Standard Notation
Change Standard to Scientific Notation
Special Cases
Practice Problems
Copyright © 2011 Lynda Greene Aguirre

3. Copyright © 2011 Lynda Greene Aguirre
Concepts and Definitions
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4. Why use Scientific Notation?
In scientific applications, there are often very large or very small numbers such as these Very large number: 53,000,000,000,000,000 Very small number:
Note: The numbers above are written in STANDARD NOTATION
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5. Why use Scientific Notation?
Trying to do calculations using such long numbers can be time consuming.
So a different way of writing these numbers was developed which is commonly called scientific notation.
Also called “exponential notation” in some textbooks
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6. Why use Scientific Notation?
The process (in a nutshell) is to shorten the number by changing the long string of leading or trailing zeros into a power of 10.
53,000,000,000,000,000
“trailing” zeros
“leading” zeros
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7. Scientific Notation Positive powers create “trailing” digits
Question: Why use a power of 10?
Positive powers create “trailing” digits
Note: Each new zero actually represents a decimal place, it might not be the number “zero” when you are using it in calculations.
The power on the ten is the same as the number of zeros on the right.
Answer: You can use it to move the decimal point to the right.
Copyright © 2011 Lynda Greene Aguirre

8. Scientific Notation Question: Why use a power of 10?
Negative Powers create “leading” digits
If you line up the “1”s, notice that each negative power moves the decimal point to the left of its previous position
Answer: You can use it to move the decimal point to the left.
Copyright © 2011 Lynda Greene Aguirre

9. What does Scientific Notation look like?
Positive or negative sign indicates BIG or SMALL number
Format:
THE EXPONENT
THE COEFFICIENT
Multiplication
symbol
Note: If the coefficient has a decimal point after the first digit, it is called “normalized”.
The position of the decimal point does not change any mathematical procedures
Copyright © 2011 Lynda Greene Aguirre

10. A missing decimal point means it’s to the right of the coefficient.
The following numbers are all written in scientific notation
A missing decimal point means it’s to the right of the coefficient.
(2 means 2.0)
Parentheses are sometimes used to indicate multiplication
Negative power means it’s a very small number
Many calculators show scientific notation this way
Zeros in between non-zero digits are included in the coefficient
EE3 means 10 to the third power
The decimal might not be after the first digit
Copyright © 2011 Lynda Greene Aguirre

11. 430,000,000 Is it a Positive or Negative Power?
Big numbers with TRAILING ZEROS have a positive power (usually not shown).
430,000,000
Trailing Zeros will have no sign on the power
No sign HERE means it’s positive
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12. Positive or Negative Sign?
Small numbers with LEADING ZEROS have a negative power
Leading Zeros will have a negative power on the “10”
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13. Scientific Notation Moving the decimal point
Note: A decimal point to the right of any number does not have to be included
Decimal moved from HERE
5 digits to the right
To HERE
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14. Changing from Scientific Notation into Standard Notation
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15. Step by Step Process 1. Write down the coefficient
Positive power - move right
The power of ten tells you how far to move
2. Move decimal point two places to the right
You can drop the decimal point if it’s to the right of the last digit
Note: You may need to fill in some zeros if there are not enough digits in the original number
Copyright © 2011 Lynda Greene Aguirre

16. Step by Step Process POSITIVE power Write down the coefficient
Move the decimal point six places to the right
Fill in some zeros if there are not enough digits in the original number
Drop the decimal point if it’s behind the last digit
Copyright © 2011 Lynda Greene Aguirre

17. Step by Step Process POSITIVE power Write down the coefficient
Move the decimal point four places to the right
Fill in some zeros if there are not enough digits in the original number
Drop the decimal point if it’s behind the last digit
Copyright © 2011 Lynda Greene Aguirre

18. Step by Step Process POSITIVE power Write down the coefficient
Move the decimal point two places to the right
No need to fill in zeros. There are enough digits in the original number
Keep the decimal point because it’s not behind the last digit
Copyright © 2011 Lynda Greene Aguirre

19. Step by Step Process Look at the NEGATIVE power
NOTE: Leave room on the left side to move the decimal
Write down the coefficient
Move the decimal point three places to the LEFT
Fill in some zeros if there are not enough digits in the original number
Keep the decimal point because it’s not behind the last digit
Copyright © 2011 Lynda Greene Aguirre

20. Step by Step Process NEGATIVE power Write down the coefficient
Move the decimal point three places to the LEFT
Fill in zeros
Keep the decimal point because it’s not behind the last digit
Copyright © 2011 Lynda Greene Aguirre

21. Step by Step Process NEGATIVE power Write down the coefficient
NOTE: Leave room on the left to move the decimal
Move the decimal point four places to the LEFT
Fill in zeros
Keep the decimal point because it’s not behind the last digit
Copyright © 2011 Lynda Greene Aguirre

22. Step by Step Process NEGATIVE power Write down the coefficient
Move the decimal two places to the LEFT
Fill in zeros
Keep the decimal point because it’s not behind the last digit
Practice Problems
Table of contents
Copyright © 2011 Lynda Greene Aguirre

23. Step by Step Process NEGATIVE power 1. Write down the coefficient
Move the decimal point one place to the LEFT
3. No need to fill in zeros. There are enough digits in the original number
Keep the decimal point because it’s not behind the last digit
Copyright © 2011 Lynda Greene Aguirre

24. Changing from Scientific Notation into Standard Notation Special Cases
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25. Zero power This is the answer ZERO power 1. Write down the coefficient
2. Decimal point doesn’t need to be moved
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26. No Decimal on Coefficient
Note: If the coefficient does not have a decimal point visible, it is “understood” to be to the right of it.
REWRITE THE COEFFICIENT TO SHOW THE POSITION OF THE DECIMAL POINT
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27. No Decimal on Coefficient
POSITIVE power
1. Write down the coefficient
Move 3 places to the right
Fill in zeros
Drop the decimal point if it’s behind the last digit
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28. Calculator Format
Note: If a different format of scientific notation is used, you can change the format or work the problem in its original form
YOU CAN REWRITE THE PROBLEM IN NORMALIZED FORM
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29. Calculator Format POSITIVE power 1. Write down the coefficient
Move 3 places to the right
Fill in zeros
Drop the decimal point if it’s behind the last digit
Copyright © 2011 Lynda Greene Aguirre

30. Different Multiplication Format
Note: If a different format of scientific notation is used, you can change the format or work the problem in its original form
YOU CAN REWRITE THE PROBLEM IN NORMALIZED FORM
Copyright © 2011 Lynda Greene Aguirre

31. Different Multiplication Format
Example:
POSITIVE power
1. Write down the coefficient
Move 3 places to the right
Fill in zeros
Drop the decimal point if it’s behind the last digit
Practice Problems
Table of contents
Copyright © 2011 Lynda Greene Aguirre

32. Changing from Standard Notation into Scientific Notation
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33. Review Number Type Location of zeros Sign of the Power SMALL NUMBERS
(decimal places)
Sign of the Power
SMALL NUMBERS
left side of the coefficient
negative power
BIG
NUMBERS
right side of the coefficient
positive power
Error Prevention Tip:
Knowing where the zeros belong will prevent students from moving the decimal in the wrong direction
Copyright © 2011 Lynda Greene Aguirre

34. Standard to Scientific Notation
Now that we know how to do this process in one direction, it is simple to reverse it.
The zeros are on the right hand side, so the power will be positive
The coefficient includes everything except the trailing zeros
Copyright © 2011 Lynda Greene Aguirre

35. Standard to Scientific Notation
Write the coefficient in normalized form
(i.e. decimal point after the first digit)
2. Write “x 10” next to it (i.e.the power of ten)
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36. Standard to Scientific Notation
3. This is a big number, so the power will be positive
Note: You can omit the “+” sign if you like, but it’s not wrong to write it down
Copyright © 2011 Lynda Greene Aguirre

37. Count decimal places This gives us the power: +8
Decimal point was not showing,
which means it’s behind the last digit
4. Count the number of digits between the new position and its old position
Decimal moved from HERE
To HERE
There are 8 digits between the new and old positions
This gives us the power: +8
Copyright © 2011 Lynda Greene Aguirre

38. Putting the pieces together
Write the coefficient in Normalized Form (decimal point after the first digit)
2. Write “x 10” next to it
Sign of the power?
zeros on the right?-positive
zeros on the left?-negative
4. How far did the decimal point move? (count digits between old and new decimal points)
Copyright © 2011 Lynda Greene Aguirre

39. Putting the pieces together
Extra digits are to the RIGHT of the coefficient
Write the coefficient in Normalized Form + 6
3. Sign of the power?
2. Write “x 10” next to it
4. How far did the decimal point move?
There are 6 digits between the new and old positions
Copyright © 2011 Lynda Greene Aguirre

40. Putting the pieces together
Extra digits are to the LEFT of the coefficient
Write the coefficient in Normalized Form - 4
3. Sign of the power?
2. Write “x 10” next to it
4. How far did the decimal point move?
There are 4 digits between the new and old positions
Copyright © 2011 Lynda Greene Aguirre

41. Putting the pieces together
Extra digits are to the RIGHT of the coefficient
Write the coefficient in Normalized Form + 8
3. Sign of the power?
2. Write “x 10” next to it
4. How far did the decimal point move?
There are 8 digits between the new and old positions
Copyright © 2011 Lynda Greene Aguirre

42. Putting the pieces together
Extra digits are to the LEFT of the coefficient
Write the coefficient in Normalized Form - 2
3. Sign of the power?
2. Write “x 10” next to it
4. How far did the decimal point move?
There are 2 digits between the new and old positions
Practice Problems
Table of contents
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43. Copyright © 2011 Lynda Greene Aguirre
Practice Problems
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44. Copyright © 2011 Lynda Greene Aguirre
Practice Problems A
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45. Copyright © 2011 Lynda Greene Aguirre
Practice Problems B
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46. End of Tutorial