1. Scientific and standard notation, conversion

2. What is Scientific Notation
A number expressed in scientific notation is expressed as a decimal number between 1 and 10 multiplied by a power of 10 (eg, 7000 = 7 x 103 or = 1.9 x 10 -6)
Why do we use it?
It’s a shorthand way of writing very large or very small numbers used in science and math and anywhere we have to work with very large or very small numbers.

3. Scientific and standard notation, conversion
Scientific Notation: expressing a number in the form c x 10n , where 1 < c < 10.
Examples: Are the following numbers written in scientific notation? a x b x 103
No, 42 is Yes greater than 10

4. Move the decimal left or right so that c is between 1 and 10
Move the decimal left or right so that c is between 1 and 10. Count the # of places you moved.
Examples: Write in scientific notation: a. 236, b c
2.36 x 105
4.325 x 10–2
7.25 x 10-4

5. Example: Write in decimal notation: a. 2.45 x 10–3 b. 1.38 x 108
To change from scientific notation back to decimal notation, move the decimal n of places, where n is the power of 10.
138,000,000
Example: Write in decimal notation: a x 10– b x 108

6. Scientific Notation Cornel Notes
Ex. 6800
Changing from Standard Notation to Scientific Notation

7. Scientific Notation Cornel Notes
Ex. 6800
Changing from Standard Notation to Scientific Notation
6800
1. Move decimal to get a number between 1 & 10 and count places moved. 3 2 1

8. Scientific Notation Cornel Notes
Ex. 6800
Changing from Standard Notation to Scientific Notation
6800
1. Move decimal to get a number between 1 & 10 and count places moved. 3 2 1
68 x 103
2. Answer is a number between 1 & 10 times the power of ten ( places moved).

9. Ex. 6800
Changing from Standard Notation to Scientific Notation
6800
1. Move decimal to get a single digit # and count places moved 3 2 1
68 x 103
2. Answer is a single digit number times the power of ten of places moved.
If the decimal is moved left the power is positive.
If the decimal is moved right the power is negative.

10. Try This
Ex. 720,000
Changing from Standard Notation to Scientific Notation

11. Try This
Ex. 720,000
Changing from Standard Notation to Scientific Notation
720000
1. Move decimal to get a single digit # and count places moved. 5 4 3 2 1

12. Try This
Ex. 720,000
Changing from Standard Notation to Scientific Notation
720000
1. Move decimal to get a single digit # and count places moved. 5 4 3 2 1
72 x 105
2. Answer is a number between 1 & 10 times the power of ten (# of places moved.

13. Scientific Notation Cornel Notes
Ex. 4.5 x 10-3
Changing from Scientific Notation to Standard Notation

14. 00045 Ex. 4.5 x 10-3 (Right if Pos. Left if Neg.) 3 2 1
Changing from Scientific Notation to Standard Notation
Ex. 4.5 x 10-3
00045
1. Move decimal the same number of places as the exponent of 10.
(Right if Pos. Left if Neg.) 3 2 1

15. Try This
Ex. 8.9 x 105
Changing from Scientific Notation to Standard Notation

16. 890000 Try This Ex. 8.9 x 105 (Right if Pos. Left if Neg.) 1 2 3 4 5
Changing from Scientific Notation to Standard Notation
890000
1. Move decimal the same number of places as the exponent of 10.
(Right if Pos. Left if Neg.) 1 2 3 4 5

17. Addition and subtraction Scientific Notation 2.0 x 102 + 3.0 x 103
1. Make exponents of 10 the same
2. Add and keep the 103 intact
The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same.
2.0 x x 105
2.0 x x 107
= x 107
= x 107
1. Make exponents of 10 the same
2. Subtract and
keep the 107 intact

18. Scientific Notation Makes These Numbers Easy
9.54x107 miles
1.86x107 miles
per second