1. Scientific Notation Algebra Seminar

2. Objectives Write numbers in standard and scientific notation.
Perform calculations with numbers in scientific notation.

3. What is Scientific Notation?
A number expressed in the form:
where
Example:
Neptune is 2,800,000,000 miles from the sun.

4. How do you write a number in scientific notation?.
Ex: 3,000,000,000,000
Where is the decimal point?
You move the decimal point to the left until the number in front of it is between 1 and 9. . .
3,000,000,000,000

5. How do you write a number in scientific notation?
Ex:
You move the decimal point to the right until the number to the left of it is between 1 and 9.
Notice that the exponent is negative!

6. Write in Scientific Notation
234,000,000
x 107
x 108
x 106
x 10-8

7. How to change numbers in scientific notation to standard notation.
First, decide which way you are going to be moving your decimal point.
Negative Exponent – move to the left
Positive Exponent – move to the right
Move the decimal point the number of the exponent.
Ex: x 104 =
1.82 x 10-5 =
63,500

8. Write in standard notation
9.608 x 109
3.5 x 10-4
8.3 x 10-2
5.07 x 106
9,608,000,000
0.083
5,070,000

9. Operations with scientific notation.
Adding:
You just add the first numbers
(4 x 104) + (9 x 104) = (4 + 9) x 104
= 13 x 104
Subtracting:
You just subtract the first numbers
(8 x 104) - (2 x 104) = (8 - 2) x 104
= 6 x 104

10. Operations with scientific notation.
Multiplying:
Multiply the first numbers and then the second numbers.
(7 x 102)(4 x 105) = (7  4)(102  105)
= 28 x 107
Write 28 in scientific notation.
(2.8 x 101) x 107
Simplify.
2.8 x 108

11. Operations with scientific notation.
Dividing:
Divide the first numbers and then the second numbers.
Simplify the exponents.