1. Scientific Notation Algebra

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.
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

10. Practice

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

12. Practice

13. 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

14. When adding or subtracting numbers in scientific notation, the exponents must be the same.
If they are different, you must move the decimal either right or left so that they will have the same exponent.

15. Moving the Decimal
For each move of the decimal to the right you have to add -1 to the exponent.
For each move of the decimal to the left you have to add +1 to the exponent.

16. Example 1
Given: 2.46 X X 103
Shift decimal 3 places to the left for 103.
Move: X 103+3
Add: 2.46 X X 106
Answer: X 106

17. Example 2
Given: X 103 – 2.65 X 10-1
Shift decimal 4 places to the right for 10-1.
Move: X 10(-1+4)
Subtract: X X 103
Answer: X 103

18. (4.12 x 106) + (3.94 x 104)
(412 x 104) + (3.94 x 104) =
x 104
Express in proper form: 4.15 x 106

19. Subtracting With Different Exponents
(4.23 x 103) – (9.56 x 102)
(42.3 x 102) – (9.56 x 102)
42.3 – 9.56 = 32.74
32.74 x 102
Express in proper form: 3.27 x 103