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Scientific Notation

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**Why use it? Width of a human hair = 0.000 008 m**

Speed of light ~ m / s Mass of a dust particle = kg

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**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

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**Which would you rather write?**

The mass of an electron is about A) kg. B) ×10−31 kg.

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**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

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**Advantages of scientific notation**

very large or very small numbers easier to work with Makes math easier calculators use it

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**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

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**I. Parts of scientific notation**

6.02 X 1023 Exponent If +, number > 0 If -, number < 0 Coefficient between 1-10

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**II. Three steps to Scientific notation**

Examples A) Coefficient Between 1 and 10 Place the decimal

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**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

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**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

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Practice time!

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13000 1.3 X 104

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4.5 X 10-6

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**71545000 7.1545 X 107 Note: rules are the same**

regardless of the number of digits! X 107 Between 1 and 10!

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**0.0045678 4.5678 X 10-3 Note: rules are the same**

regardless of the number of digits! X 10-3

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**Note: zeros between numbers**

don’t change the rules! 9.209 X 106

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**Note: zeros between numbers**

don’t change the rules! 4.005 X 10-5

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**3.21 X 103 3210 Challenge! Can you go backwards?**

HINT: reverse the rules! Reverse the steps! 3.21 X 103 3210

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**3.21 X 10-3 .00321 Challenge! Can you go backwards?**

HINT: reverse the rules! Reverse the steps! 3.21 X 10-3 .00321

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**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

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**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

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**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

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