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Scientific Notation

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

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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 X 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? A) electrons/mole X kg/electron What is the mass, in kg, of a mole of electrons? ×10 31 kg/electron X 6.02 X electrons/mole 0000

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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 –1–10 X 1 = 10 = (1 ten)= 10 1 –1–10 X 10 = 100 = (2 tens) = 10 2 –1–10 X 10 x 10 = 1000 = (3 tens) = 10 3 –1–10 X 10 X 5 = 500 = (2 tens) = 5 X 10 2 –1–10 X 10 X 10 X 3.14 = 3140 (3 tens) = 3.14 X 10 3

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

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

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StepsExamples B) Count and Erase –Count spaces to move decimal –Note direction –Erase extra zeros jumps left jumps right

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StepsExamples C) Exponent –# spaces = power of 10 –Direction left = + –Direction right = jumps left 4 jumps right X X 10 -4

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Practice time!

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X 10 4

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X 10 -6

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X 10 7 Note: rules are the same regardless of the number of digits! Between 1 and 10!

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X Note: rules are the same regardless of the number of digits!

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X 10 6 Note: zeros between numbers dont change the rules!

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X Note: zeros between numbers dont change the rules!

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

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

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V. Math with Scientific Notation A)Multiplication Multiply coefficients Add exponents Adjust answer StepsExamples (5 X 10 2 ) X (3 X 10 6 ) 5 X 3 = = 8 15 X X 10 9 (3.2 X ) X (4 x 10 5 ) 3.2 X 4 = = X X 10 4

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B) Division Divide coefficients subtract exponents adjust answer StepsExamples (6 X 10 2 ) (3 X 10 6 ) 6 / 3 = = -4 2 X (1.6 X ) / (8 x 10 5 ) 1.6 / 8 = = X X 10 -6

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StepsExamples C) Addition and Subtraction Adjust so exponents are the same add or subtract coefficients adjust answer (6 X 10 2 ) + (3 X 10 4 ) (6 X 10 2 ) + (300 X 10 2 ) 306 X X 10 4

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