1. Adding/Subtracting/Multiplying/Dividing Numbers in Scientific Notation

2. A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer

3. An easy way to remember this is:
If an exponent is positive, the number gets larger, so move the decimal to the right.
If an exponent is negative, the number gets smaller, so move the decimal to the left.

4. Adding/Subtracting when Exponents are Equal
When the exponents are the same for all the numbers you are working with, add/subtract the base numbers then simply put the given exponent on the 10.

5. General Formulas (N X 10x) + (M X 10x) = (N + M) X 10x
(N X 10y) - (M X 10y) = (N-M) X 10y

6. Example 1 Given: 2.56 X 103 + 6.964 X 103 Add: 2.56 + 6.964 = 9.524
Answer: X 103

7. Example 2
Given: 9.49 X 105 – X 105
Subtract: 9.49 – = 4.627
Answer: X 105

8. Adding With the Same Exponent
(3.45 x 103) + (6.11 x 103)
= 9.56
9.56 x 103

9. Subtracting With the Same Exponent
(8.96 x 107) – (3.41 x 107)
8.96 – 3.41 = 5.55
5.55 x 107

10. Adding/Subtracting when the Exponents are Different

11. 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.

12. 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.

13. Continued…
It does not matter which number you decide to move the decimal on, but remember that in the end both numbers have to have the same exponent on the 10.

14. 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

15. 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

16. (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

17. 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

18. Multiplying… The general format for multiplying is as follows…
(N x 10x)(M x 10y) = (N)(M) x 10x+y
First multiply the N and M numbers together and express an answer.
Secondly multiply the exponential parts together by adding the exponents together.

19. Multiplying…
Finally multiply the two results for the final answer.
(2.41 x 104)(3.09 x 102)
2.41 x 3.09 = 7.45
4 + 2 = 6
7.45 x 106

20. 7) evaluate (3,600,000,000)(23). The answer in scientific notation is
8.28 x 10 10
The answer in decimal notation is
82,800,000,000

21. 6) evaluate (0.0042)(330,000). The answer in decimal notation is 1386
The answer in scientific notation is
1.386 x 103

22. Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

23. Dividing… The general format for dividing is as follows…
(N x 10x)/(M x 10y) = (N/M) x 10x-y
First divide the N number by the M number and express as an answer.
Secondly divide the exponential parts by subtracting the exponent from the exponent in the upper number.

24. Dividing…
Finally divide the two results together to get the final answer.
(4.89 x 107)/(2.74 x 104)
4.89 / 2.74 = 1.78
7 – 4 = 3
1.78 x 103

25. 5) evaluate: x x 102 :
The answer in scientific notation is
6 x
The answer in decimal notation is

26. 0.0028125 Write in scientific notation. 2.8125 x 10-3
4) Evaluate: x x 10-2
Write in scientific notation.
x 10-3