1. Adding and Subtracting Numbers in Scientific Notation

2. Adding/Subtracting when Exponents are Equal
When the exponents are the same: easy peasy:
just add/subtract the numbers then carry the base 10 and the exponent through.

3. If the Exponents are the same:
When adding
or subtracting numbers in scientific notation, the exponents must be the same.
2.46 X X 103
2.46 X X 103
X 103
Then just rearrange the numbers and carry through the Power of 10

4. Example 1
2.56 X X 103
Given: 2.56 X X 103
= 9.524
Answer: X 103

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

6. Adding/Subtracting when the Exponents are Different

7. If the Exponents are different:
Turn the expression into Standard Notation
Calculate
Turn the result back into Scientific Notation

8. Example 1
Given: 2.46 X X 103
Turn problem into Standard Notation: 2.46 X 106 = 2,460,000
3.476 X 103 = 3,476
Calculate:
2,460, ,476 = 2,463,476
Turn answer into Scientific Notation: X 106

9. Example 2
Given: X 103 – 2.65 X 10-1
Turn problem into Standard Notation: X 103 = 5,762
2.65 X 10-1 = .265
Calculate:
5, =
Turn answer into Scientific Notation: X 103

10. Need a Challenge??
(You can skip this part if you want and do the problems at the end)
When adding or subtracting numbers in scientific notation, the exponents must be the same.
Therefore…………
If they are different, you must move the decimal either right or left so that they will have the same exponent.

11. Need a Challenge?? …continued
It does not matter which number you use to change the exponent, but remember that before you can do the calculation, both Powers of 10 have to have the same exponent on the 10.

12. Need a Challenge?? …continued
Remember!!!
For each move of the decimal to the right,
you have to add -1 to the exponent X 103 = 3.0 X 102
For each move of the decimal to the left,
you have to add +1 to the exponent.
0.3 X 103 = X 104

13. Need a Challenge?? …continued
Same problem as before!
Given: X 103 – 2.65 X 10-1
X 10(-1+4)
Subtract: X X 103
X 103
Answer: X 103
Exponents don’t match!
Shift decimal 4 places to the left for to become 103.

14. Need a Challenge?? …continued
Same problem as before!
Given: 2.46 X X 103
X 103+3
Add: 2.46 X X 106
Answer: X 106
Shift decimal 3 places to the left for 106. .

15. Need a Challenge?? …continued
Try a new problem!
Given: 7.4 X X 106
X 10(2+4)
Add: X X 106
X 106
Answer: X 106
Shift decimal 4 places to the left for 106. .

16. Practice Worksheet (solve using either method)
2 × × 104 =
7 × 105 – 5.2 × 104 =
3.4 x x 103 =
8.41 x 10-5 – 7.9 x 10-6 =
3.8 x 104
6.48 x 105
4.91 x 103
7.62 x 10-5