1. Scientific Notation

2. Why use it? Width of a human hair = 0.000 008 m
Speed of light ~ m / s
Mass of a dust particle = kg

3. Which would you rather write?
The mass of the earth is 5,973,600,000,000,000,000,000,000 kg
The mass of the earth is X 1024 kg

4. Which would you rather write?
The mass of an electron is about
A)  kg.
B) ×10−31 kg.

5. Which would you rather calculate?
What is the mass, in kg, of a mole of electrons?
A) electrons/mole
X  kg/electron
×10−31 kg/electron X X 1023 electrons/mole

6. Advantages of scientific notation
very large or very small numbers easier to work with
Makes math easier
calculators use it

7. How it works Base 10 decimal number system 10 X 1 = 10 = (1 ten)= 101
10 X 10 = 100 = (2 tens) = 102
10 X 10 x 10 = 1000 = (3 tens) = 103
10 X 10 X 5 = 500 = (2 tens) = 5 X 102
10 X 10 X 10 X 3.14 = 3140 (3 tens) = 3.14 X 103

8. I. Parts of scientific notation
6.02 X 1023
Exponent
If +, number > 0
If -, number < 0
Coefficient
between 1-10

9. II. Three steps to Scientific notation
Examples
A) Coefficient
Between 1 and 10
Place the decimal

10. Steps Examples B) Count and Erase 5 7 6 0 0 0 5 7 6 0 0 0
Count spaces to move decimal
Note direction
Erase extra zeros
5 jumps left
4 jumps right

11. Steps Examples C) Exponent 5 7 6 0 0 0. 5. 7 6 X 105 0 . 0 0 0 5 7 6
# spaces = power of 10
Direction left = +
Direction right = -
5. 7 6
X 105
5 jumps left
5.7 6
X 10-4
4 jumps right

12. Practice time!

13. 13000
1.3 X 104

14.
4.5 X 10-6

15. 71545000 7.1545 X 107 Note: rules are the same
regardless of the number of digits!
X 107
Between 1 and 10!

16. 0.0045678 4.5678 X 10-3 Note: rules are the same
regardless of the number of digits!
X 10-3

17. Note: zeros between numbers
don’t change the rules!
9.209 X 106

18. Note: zeros between numbers
don’t change the rules!
4.005 X 10-5

19. 3.21 X 103 3210 Challenge! Can you go backwards?
HINT: reverse the rules!
Reverse the steps!
3.21 X 103
3210

20. 3.21 X 10-3 .00321 Challenge! Can you go backwards?
HINT: reverse the rules!
Reverse the steps!
3.21 X 10-3
.00321

21. V. Math with Scientific Notation
Steps
Examples
Multiplication
Multiply coefficients
Add exponents
Adjust answer
(5 X 102 ) X (3 X 106)
5 X 3 = = 8
15 X 108 
1.5 X 109
(3.2 X 10-2) X (4 x 10 5)
3.2 X 4 = = 3
12.8 X 103
1.28 X 104

22. Steps Examples B) Division (6 X 102 ) ∕ (3 X 106) Divide coefficients
subtract exponents
adjust answer
(6 X 102 ) ∕ (3 X 106)
6 / 3 = = -4
2 X 10-4
(1.6 X 10-2) / (8 x 10 5)
1.6 / 8 = = -7
0.2 X 10-7 
2.0 X 10-6

23. Steps Examples C) Addition and Subtraction Adjust so exponents
are the same
add or subtract
coefficients
adjust answer
(6 X 102 ) + (3 X 104)
(6 X 102 ) + (3 X 104)
(6 X 102 ) + (300 X 102)
306 X 102
3.06 X 104