1. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
ADDITION AND SUBTRACTION

2. Review: M x 10n Scientific notation expresses a number in the form:
n is an integer
1  M  10

3. IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
4 x 106
+ 3 x 106
_______________ 7
x 106

4. IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
4 x 106
+ 3 x 106
_______________ 7
x 106

5. If the exponents are NOT the same, we must move a decimal to make them the same.

6. 4.00 x 106
4.00 x 106
x 105
+ .30 x 106
4.30
x 106
Move the decimal on the smaller number!

7. A Problem for you…
2.37 x 10-6
x 10-4

8. Solution…
x 10-6
2.37 x 10-6
x 10-4

9. Solution…
x 10-4
x 10-4
x 10-4

10. Addition and subtraction Scientific Notation 2.0 x 102 + 3.0 x 103
1. Make exponents of 10 the same
2. Add and keep the 103 intact
The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same.
2.0 x x 105
2.0 x x 107
= x 107
= x 107
1. Make exponents of 10 the same
2. Subtract and
keep the 107 intact

11. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
MULTIPLYING AND DIVIDING

12. Rule for Multiplication
When multiplying with scientific notation:
Multiply the coefficients together.
Add the exponents.
The base will remain 10.

13. (2 x 103) • (3 x 105) =
6 x 108

14. (9.2 x 105) x (2.3 x 107) =
21.16 x 1012 =
2.116 x 1013

15. (3.2 x 10-5) x (1.5 x 10-3) =
4.8 • 10-8

16. Rule for Division
When dividing with scientific notation
Divide the coefficients
Subtract the exponents.
The base will remain 10.

18. (8 • 106) ÷ (2 • 103) =
4 x 103

19. (3.402 x 105) ÷ (6.3 x 107) =
0.54 x 10-2

20. Please multiply the following numbers.
(5.76 x 102) x (4.55 x 10-4) =
(3 x 105) x (7 x 104) =
(5.63 x 108) x (2 x 100) =
(4.55 x 10-14) x (3.77 x 1011) =
(8.2 x10-6) x (9.4 x 10-3) =

21. Please multiply the following numbers.
(5.76 x 102) x (4.55 x 10-4) =
2.62 x 10-1
(3 x 105) x (7 x 104) =
2.1 x 1010
(5.63 x 108) x (2 x 100) =
1.13 x 109
(4.55 x 10-14) x (3.77 x 1011) =
1.72 x 10-2
(8.2 x10-6) x (9.4 x 10-3) =
7.71 x 10-8

22. Please divide the following numbers.
(5.76 x 102) / (4.55 x 10-4) =
(3 x 105) / (7 x 104) =
(5.63 x 108) / (2) =
(8.2 x 10-6) / (9.4 x 10-3) =
(4.55 x 10-14) / (3.77 x 1011) =

23. Please divide the following numbers.
(5.76 x 102) / (4.55 x 10-4) = 1.27 x 106
(3 x 105) / (7 x 104) = 4.3 x 100 = 4.3
(5.63 x 108) / (2 x 100) = x 108
(8.2 x 10-6) / (9.4 x 10-3) = 8.7 x 10-4
(4.55 x 10-14) / (3.77 x 1011) = 1.2 x 10-25

24. Scientific Notation Makes These Numbers Easy
9.54x107 miles
1.86x107 miles
per second