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Scientific Notation & Significant Figures

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Scientific Notation Why do we need it? It makes it much easier to write extremely large or extremely small numbers.

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Scientific Notation What would you rather write? 602,200,000,000,000,000,000,000 Or 6.02 x 10 23

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Scientific Notation 6.02 x 10 23 Writing the number like this means you will take the number 6.02 and multiply it by 10 twenty three times

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Scientific Notation Every time the decimal moves left or right one place it is divided or multiplied by ten.

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Scientific Notation 10 1 = 10 10 3 = 1,000 10 5 = 100,000 10 -1 = 0.1 10 -3 =0.01 10 -5 = 0.00001

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Scientific Notation 1. Move the decimal so that there is only one non zero number in front of it 5,050,000,000

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Scientific Notation 1. Move the decimal so that there is only one non zero number in front of it 5,050,000,000 5.050000000

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Scientific Notation 1.Move the decimal so that there is only one non zero number in front of it 2.Count how many places the decimal had to move 5.050000000 9

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Scientific Notation 1.Move the decimal so that there is only one non zero number in front of it 2.Count how many places the decimal had to move 3.This number now becomes the exponent in the scientific notation. If the decimal moved to the left the exponent is positive, if it moved to the right the exponent is negative. 5.05 x 10 9

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5,050,000,000 5.05 x 10 9 Equals They are the same number

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Try a really small number 0.0000000122 Write this number in scientific notation.

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Try a really small number 0.0000000122 1.22

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The decimal moved left how many spaces? 0.00000001.22 Write this number as the exponent. 8 1.22 x 10 -8

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Significant Figures

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Sig Figs answer the question of How many places should I round to? or How many decimals do I keep?

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Accuracy how close a measurement is to the true value of the quantity measured Precision the exactness of a measurement

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The number of sig figs you keep in an answer totally depends on the precision and accuracy of the instruments you are using.

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Rules to find Sig Figs 1.If the Number is not a zero it is significant 2.If zeros are in between two non zero numbers it is significant 3.Zeros before a non zero number are not significant. 4. Zeros after non zero numbers are significant only if there is a decimal.

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352 4505 0.00324 1240 130.0

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When Multiplying/Dividing keep the smallest number of sig figs in the answer. When Adding/Subtracting keep the smallest number of decimals in the answer.

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Dimensional Analysis: A mathematical tool used to convert from one type of unit to another type of unit

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Situation: Situation: You need to change $50 dollars into nickels. How many nickels do you need ???

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We need a plan of attack! 1. Write down what we are given $50 dollars

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We need a plan of attack! 1. Write down what we are given 2. Find a common ratio $1 dollar = 20 nickels

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1. Write down what we are given 2. Find a common ratio $1 dollar = 20 nickels We need a plan of attack! 3. Place the ratio in the chart so that unit that is in the given is on the bottom

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$50 dollars 20 nickels $1 dollar

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1. Write down what we are given 2. Find a common ratio $1 dollar = 20 nickels We need a plan of attack! 3. Place the ratio in the chart so that unit that is in the given is on the bottom 4. Simplify!!!

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$50 dollars 20 nickels $1 dollar Simplify means cancel out units and do the math. On top multiply on bottom divide 1000 nickels