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