Scientific Notation
Why use it?
Width of a human hair = 0.000 008 m
Speed of light ~ 300 000 000 m / s
Mass of a dust particle = 0.000 000 000 753 kg
Which would you rather write?
a) The mass of the earth is 5,973,600,000,000,000,000,000,000 kg
b) The mass of the earth is 5.9736 X 1024 kg
Which would you rather write?• The mass of an electron is about
• A) 0.000 000 000 000 000 000 000 000 000 000 910 938 26 kg.
• B) 9.1093826×10−31 kg.
Which would you rather calculate?
A) 602000000000000000000000 electrons/mole
X 0.00000000000000000000000000000091093826 kg/electron
What is the mass, in kg, of a mole of electrons?
9.1093826×10−31 kg/electron X 6.02 X 1023 electrons/mole
0000
Advantages of scientific notation
•very large or very small numbers easier to work with
•Makes math easier
•calculators use it
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
I. Parts of scientific notation
6.02 X 1023
Coefficientbetween 1-10
ExponentIf +, number > 0If -, number < 0
II. Three steps to Scientific notation
A) Coefficient– Between 1 and 10– Place the decimal
Steps Examples5 7 6 0 0 0
5 7 6 0 0 0
0 0 0 0 5 7 6
0 0 0 0 5 7 6
Steps ExamplesB) Count and Erase
– Count spaces to move decimal
– Note direction– Erase extra zeros
5 7 6 0 0 0
5 7 6 0 0 0
5 jumps left
0 0 0 0 5 7 6
0 0 0 0 5 7 6
4 jumps right
Steps ExamplesC) Exponent
– # spaces = power of 10– Direction left = +– Direction right = -
5. 7 6
5 jumps left
4 jumps right
X 105
5 7 6 0 0 0.
0 . 0 0 0 5 7 6
5.7 6 X 10-4
Practice time!
13000
1.3 X 104
0.0000045
4.5 X 10-6
71545000
7.1545 X 107
Note: rules are the same regardless of the number of digits!
Between 1 and 10!
0.0045678
4.5678 X 10-3
Note: rules are the same regardless of the number of digits!
9209000
9.209 X 106
Note: zeros between numbers don’t change the rules!
0.00004005
4.005 X 10-5
Note: zeros between numbers don’t change the rules!
3.21 X 103
3210
Challenge! Can you go backwards?HINT: reverse the rules!
Reverse the steps!
3.21 X 10-3
.00321
Challenge! Can you go backwards?HINT: reverse the rules!
Reverse the steps!
V. Math with Scientific Notation
A) MultiplicationMultiply coefficients
Add exponents
Adjust answer
Steps Examples
(5 X 102 ) X (3 X 106)
5 X 3 = 15 2+6 = 8
15 X 108 1.5 X 109
(3.2 X 10-2) X (4 x 10 5)
3.2 X 4 = 12.8 -2+5 = 3
12.8 X 103 1.28 X 104
B) Division
Divide coefficients
subtract exponents
adjust answer
Steps Examples
(6 X 102 ) ∕ (3 X 106)
6 / 3 = 2 2-6 = -4
2 X 10-4
(1.6 X 10-2) / (8 x 10 5)
1.6 / 8 = 0.2 -2-5 = -7
0.2 X 10-7 2.0 X 10-6
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