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? The mass of the earth is 5,973,600,000,000,000,000,000,000 kg 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? What is the mass, in kg, of a mole of electrons? A) 602000000000000000000000 electrons/mole X 0.00000000000000000000000000000091093826 kg/electron 9.1093826×10−31 kg/electron X 6.02 X 1023 electrons/mole

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 Exponent If +, number > 0 If -, number < 0 Coefficient between 1-10

II. Three steps to Scientific notation Examples A) Coefficient Between 1 and 10 Place the decimal 5 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 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 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 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 0 0 0. 5. 7 6 X 105 5 jumps left 0 . 0 0 0 5 7 6 5.7 6 X 10-4 4 jumps right

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! 71545000 7.1545 X 107 Between 1 and 10!

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

Note: zeros between numbers don’t change the rules! 9209000 9.209 X 106

Note: zeros between numbers don’t change the rules! 0.00004005 4.005 X 10-5

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

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

V. Math with Scientific Notation Steps Examples Multiplication Multiply coefficients Add exponents Adjust answer (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

Steps Examples B) Division (6 X 102 ) ∕ (3 X 106) Divide coefficients subtract exponents adjust answer (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