1. Scientific Notation

2. Scientific Notation

3. Scientific Notation COEFFICIENT It must be more than 1 but
less than 10

4. Scientific Notation BASE COEFFICIENT It must be more than 1 but
less than 10
BASE

5. Scientific Notation BASE COEFFICIENT It must be more than 1 but
THE EXPONENT or POWER OF TEN
COEFFICIENT
It must be
more than 1 but
less than 10
BASE

6. Scientific notation: A method for expressing, and working with, very large or very small numbers. 
Copyright © 2010 Ryan P. Murphy

7. Scientific notation: A method for expressing, and working with, very large or very small numbers. 
Copyright © 2010 Ryan P. Murphy

8. “5 point 7 times ten to the sixth power”

9. To write a number in scientific notation:
Put a decimal point after the first digit and drop the zeroes.
146,000,000 = 1.46

10. Note that the places start after the decimal point
To find the exponent, count the number of places from the decimal to the end of the numbers.
In there are 8 places.
Therefore we write 146,000,000 as 1.46 x 108
Note that the places start after the decimal point

11. What is 567,000 in scientific notation?
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12.
5.67 x 105

13. What is 40,100,000,000,000 in scientific notation?
This is the distance from earth to the nearest star Proxima Centauri.
Copyright © 2010 Ryan P. Murphy

14. Answer! 40,100,000,000,000 = 4.01 x 1013
Copyright © 2010 Ryan P. Murphy

15. What is 8,000,000,000 in scientific notation?
A projection for the number of people on earth!
Copyright © 2010 Ryan P. Murphy

16. Answer! 8,000,000,000 = 8 x 109
Copyright © 2010 Ryan P. Murphy

17. What is 9.9 x 107? - Work in the opposite direction
This is the distance from the Earth to Mars in Kilometers.
Copyright © 2010 Ryan P. Murphy

18. Answer! 9.9 x 107 = 99,000,000
There needs to be six places after the decimal. Since the .9 is the first, you would add 6 zeroes to equal 107.

19. What is x 105 ?
The distance in kilometers from the Earth to the Moon.

20. Answer! x is 384,400 km

21. Scientific notation can be used for very small numbers as well.
The decimal number written in scientific notation would be 6.5 x 10-7
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22. What is 0.00053 in scientific notation?
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23. Answer! = 5.3 x 10-4
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24. What is 0.00000042 in scientific notation?
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25. Answer! is 4.2 × 10-7
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26. What is 9,780,000,000,000,000,000,000,000,000 in scientific notation?
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27. Answer!
9,780,000,000,000,000,000,000,000,000
9.78 x 1027
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28. What is (2 x 104) x (4 x 103) ?
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29. What is (2 x 104) (4 x 103) ? What is (2 x 104) (4 x 103)
1) Multiply the coefficients
2) Add the exponents (base 10 remains)
What is (2 x 104) (4 x 103)
Copyright © 2010 Ryan P. Murphy

30. What is (2 x 104) (4 x 103) ? Answer! 8 x 107 or 80,000,000
Copyright © 2010 Ryan P. Murphy

31. Write these numbers using the scientific notation
DO THE PROBLEMS
Write these numbers using
the scientific notation
35 x 10 5 = 3.5 x 10 6
6 x 10 −10
9.7 x 10 −3
1.7 x 10 8

32. What is (3 x 104)/(2 x 103) ?
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33. 2) Subtract the exponents (base 10 remains)
What is (3 x 104) / (2 x 103) ?
1) Divide the coefficients
2) Subtract the exponents (base 10 remains)
What is (2 x 104) (4 x 103)
Copyright © 2010 Ryan P. Murphy

34. What is (3 x 104) / (2 x 103) ? What is (2 x 104) (4 x 103)
1) Multiply the coefficients
2) Subtract the exponents (base 10 remains)
Example 1: (3 x 104) / (2 x 103) = 1.5 x 101
What is (2 x 104) (4 x 103)
Copyright © 2010 Ryan P. Murphy

35. DO THE PROBLEMS
Write these numbers using the scientific notation. Round them to 2 decimal places,
1.50 x 10 −2
3.50 x 10 −15
0.50 x 10 −11 = 5.00x 10 −12
3.75 x 10 12

36. Scientific Notation exercise
How do you solve this??
(3.0 x 104) + (2.0 x 103) =

37. Scientific Notation exercise
How do you solve this??
(3.0 x 104) + (2.0 x 103) =
(30.0 x 103) + (2.0 x 103) =

38. Scientific Notation exercise
How do you solve this??
(3.0 x 104) + (2.0 x 103) =
(30.0 x 103) + (2.0 x 103) =

39. Scientific Notation exercise
How do you solve this??
(3.0 x 104) + (2.0 x 103) =
(30.0 x 103) + (2.0 x 103) =
32 x 10?

40. Scientific Notation exercise
How do you solve this??
(3.0 x 104) + (2.0 x 103) =
(30.0 x 103) + (2.0 x 103) =
32 x 10?

41. Scientific Notation exercise
How do you solve this??
(3.0 x 104) + (2.0 x 103) =
(30.0 x 103) + (2.0 x 103) =
32 x 10?

42. Scientific Notation exercise
How do you solve this??
(3.0 x 104) + (2.0 x 103) =
(30.0 x 103) + (2.0 x 103) =
32 x 103

43. Scientific Notation exercise
How do you solve this??
(3.0 x 104) + (2.0 x 103) =
(30.0 x 103) + (2.0 x 103) =
32 x 103 = 3.2 x 104