1. Warm up
A son weighs 76 lbs. His father weighs 266 lbs. How many times greater does the father weigh than his son?
3.5 times greater

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 coefficients
Step 2 – Bring down the given exponent on the base 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
8.0 x 103
8.0 x 106
8.0 x 10-3
8.53 x 103
The exponents are the same, so add the coefficients.

8. (8.0 x 103) – (2.0 x 103 )
6.0 x 10-3
6.0 x 100
6.0 x 103
7.8 x 103

9. 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.

10. 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.

11. Adding/Subtracting when the Exponents are DIFFERENT
Step 1 – Rewrite so the exponents are the same Step 2 - add/subtract the coefficient Step 3 – Bring down the given exponent on the base 10
← moving the decimal to the left
10x gets bigger (add)
moving the decimal to the right→
10x gets smaller (subtract)

12. 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

13. 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

14. 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 coefficients =
2.4634
Step 3 – Bring Down Exponents
X 106

15. 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 exponent
5.762 X 103

16. (7.0 x 103 ) + (2.0 x 102 ) is
9.0 x 103
9.0 x 105
7.2 x 103
7.2 x 102

17. (7.8 x 106 ) – (3.5 x 105 ) is
4.3 x 104
4.3 x 1010
7.45 x 106

18. 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.

19. Classwork – Write the problem and the answer Turn in when completed
(3.45 x 103) + (6.11 x 103)
(4.12 x 106) + (3.94 x 104)
(8.96 x 107) – (3.41 x 107)
(4.23 x 103) – (9.56 x 102)
(3.078 x 1010) ÷ (3.8 x 105)
(1.479 x 102) ÷ (5.1 x 10-2)
(5.8 x 1010) x (9.7 x 103)
(1.5 x 106) x (8.1 x 102)

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