1. Adding and Subtracting Numbers in Scientific Notation
January 2, 2014

2. When adding or subtracting numbers in scientific notation, the exponents must be the same.

3. Adding/Subtracting when Exponents are THE SAME
Step 1 - add/subtract the decimal
Step 2 – Bring down the given exponent on the 10

4. Step 2 – Bring down exponent :
Example 1
(2.56 X 103) + (6.964 X 103)
Step 1 - Add: =
9.524
Step 2 – Bring down exponent :
9.524 x 103

5. Step 2 – Bring down exponent:
Example 2
(9.49 X 105) – (4.863 X 105)
Step 1 - Subtract:
9.49 – =
4.627
Step 2 – Bring down exponent:
4.627 x 105

6. Adding/Subtracting when the Exponents are DIFFERENT
When adding or subtracting numbers in scientific notation, the exponents must be the same.
If they are different, you must move the decimal so that they will have the same exponent.

7. Moving the Decimal
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.

8. Adding/Subtracting when the Exponents are DIFFERENT
Step 1 – Rewrite so the exponents are the same Step 2 - add/subtract the decimal Step 3 – Bring down the given exponent on the 10

9. Example 3
(2.46 X 106) + (3.4 X 103)
Step 1 – Rewrite with the same exponents
3.4 X 103 
X 103+3
New Problem: (2.46 X 106) + ( X 106)
Step 2 – Add decimals =
2.4634
Step 3 – Bring Down Exponents
X 106

10. Example 4
(5.762 X 103) – (2.65 X 10-1)
Step 1 – Rewrite with the same exponents
2.65 X 10-1 
X 10(-1+4)
New Problem : (5.762 X 103) – ( X 103)
Step 2 – Subtract Decimals
5.762 – =
5.762
Step 3 – Bring down decimals
5.762 X 103

11. Practice (3.45 x 103) + (6.11 x 103) (4.23 x 103) – (9.56 x 102)