1. Adding and Subtracting Numbers in Scientific Notation
Created by: Langan, Kansky, Nizam, O’Donnell, and Matos

2. Using Scientific Notation in Multiplication, Division, Addition and Subtraction
Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.

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

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

5. 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

6. 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

7. The sum of 5.6 x 103 and 2.4 x 103 is A 8.0 x 103 B 8.0 x 106 C
Answer: A

8. The exponents are the same, so add the coefficients.
The sum of 5.6 x 103 and 2.4 x 103 is A
8.0 x 103 B
8.0 x 106 C
8.0 x 10-3 D
8.53 x 103
The exponents are the same, so add the coefficients.
Answer: A

9. 8.0 x 103 minus 2.0 x 103 is A
6.0 x 10-3 B
6.0 x 100 C
6.0 x 103 D
7.8 x 103
Answer: C

10. 8.0 x 103 minus 2.0 x 103 is A
6.0 x 10-3 B
6.0 x 100 C
6.0 x 103 D
7.8 x 103
Answer: C

11. 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.

12. 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.

13. 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

14. Adding With Different Exponents
(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

15. 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

16. 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

17. 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

18. 7.0 x 103 plus 2.0 x 102 is A
9.0 x 103 B
9.0 x 105 C
7.2 x 103 D
7.2 x 102
Answer: C

19. 7.0 x 103 plus 2.0 x 102 is A
9.0 x 103 B
9.0 x 105 C
7.2 x 103 D
7.2 x 102
Answer: C

20. 7.8 x 105 minus 3.5 x 104 is A
7.45 x 105 B
4.3 x 104 C
4.3 x 106 D
4.3 x 1010
Answer: A

21. 7.8 x 105 minus 3.5 x 105 is A
7.45 x 105 B
4.3 x 104 C
4.3 x 106 D
4.3 x 1010
Answer: A

22. Adding and Subtracting…
The important thing to remember about adding or subtracting is that the exponents must be the same!
If the exponents are not the same then it is necessary to change one of the numbers so that both numbers have the same exponential value.

23. Practice (3.45 x 103) + (6.11 x 103) (4.12 x 106) + (3.94 x 104)