1. Ch 8: Exponents E) Scientific Notation
Objective:
To simplify expressions involving scientific notation.

2. Key concepts: Write expressions in Standard Form
Write expressions in Scientific Notation
Multiply scientific notation expressions
Divide scientific notation expressions

3. Definitions Scientific Notation
used to write very large or very small numbers
expressed in the form:
an integer
a number between 1.0 and 9.9
Standard Form
An expression written without exponents

4. Rules
From Standard Form to Scientific Notation
1) Determine where the decimal should be placed
2) Count how many places from the “new” decimal
point to the “old” decimal point
To the RIGHT = (+) positive exponent
To the LEFT = (−) negative exponent
3,780,000,000,000 =
Example 1
12 jumps to the right
Example 2 =
7 jumps to the left

5. Classwork 1)
46,000,000 =
7 jumps to the right 2)
620,000,000,000 =
11 jumps to the right 3) =
4 jumps left 4) =
6 jumps left

6. Rules
From Scientific Notation to Standard Form
Move the current decimal point the number of
places based on the exponent as follows:
(+) positive exponent = to the RIGHT
(−) negative exponent = to the LEFT
3.6 =
360,000
Example 1
8.43
Example 2 =

7. Classwork 5)
2.64 =
2,640,000,000
3.41 = 6) 7) 4 =
400,000,000 8) 7 =

8. Rules Multiply the numbers that have no exponents.
Multiplying Scientific Notation expressions
Multiply the numbers that have no exponents.
2) Add the exponents to calculate the new exponent for 10.
3) Verify that the result is in scientific notation
an integer
a number between 1.0 and 9.9

9. Example 1
Example 2
(5.63)(3.4)
19.142
107+8
(2.1)(1.5) +1
bigger
3.15
108+6
smaller
1 jump right
Not in
Scientific Notation

10. Classwork 9) 10) 11) 12) +1 smaller bigger 1 jump right +1 smaller

11. Rules Divide the numbers that have no exponents.
Dividing Scientific Notation expressions
Divide the numbers that have no exponents.
2) Subtract the exponents to calculate the new exponent for 10.
3) Verify that the result is in scientific notation
an integer
a number between 1.0 and 9.9

12. Example 1
Example 2 = = −1 = =
smaller
bigger
1 jump left =

13. Classwork
13) = −1
14) =
bigger
smaller
1 jump left =