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Significant Figures

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Who cares? Sig Figs measure the degree of precision of a measurement.

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But first: What’s the difference between accuracy and precision? Do they mean the same thing?

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Important definitions: accuracy: a measure of how closely a measurement agrees with the correct or true value precision: a measure of how closely individual measurements agree with one another

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Example question: Two students measured the mass of a small pebble, which had an actual mass of 2.35 grams. Sally’s measurements were 2.78 grams, 2.82 grams, and 2.81 grams. Madison’s measurements were 2.30 grams, 2.34 grams, and 2.41 grams. Which student was more accurate? Which student was more precise?

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A correctly precise measurement includes all digits that are known for sure, plus a digit that is estimated.

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For example:

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Another example:

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Rules for counting sig figs: There are ONLY two rules to remember when counting the # of Sig Figs.

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Rule #1: Don’t start counting till you get to a number that isn’t a zero. Rule #2: Once you start counting, don’t stop till you’ve counted all the digits, including zeroes.

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And you need to remember a little geography: Where is the Atlantic Ocean, and where is the Pacific Ocean?

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How many sig figs are in this number: 273.5200? Ask yourself: Is the decimal point present or absent?

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Answer: Present Count from first non-zero number starting at the Pacific side. 273.5200 Once you start counting, you don’t stop!

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Examples 2.553 S.F. 0.25004 S.F. 100.25 5 S.F.

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Examples 12.50 0.0050 0.0003

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The first step is always to ask yourself: Is the decimal point present or absent? 18,000,000

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Answer: Absent Count from first non-zero number moving from the Atlantic side. 18,000,000

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Examples 1353 S.F. 1001 S.F. 10500 3 S.F.

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Examples 3500.0020 17,50027.02 135.0 2060

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Using sig figs in calculations

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For multiplication and division:

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Your answer can not be more precise than the least precise measurement.

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Think of Sloppy Joe

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You and your lab partner, Sloppy Joe, have been assigned to find the area of your lab table. You carefully measure the length, and find it to be 233.65 cm. Sloppy Joe casually slides the meter stick along the width, suggests that it measures about 200 cm.

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233.65 x 200 = 46730 5 S.F.1 S.F.4 S.F.? Answer must be recorded as 50,000 cm 2 It can have only one sig fig.

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Your answer MUST have the same number of sig figs as the factor with the least number of sig figs.

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610 x 6.20 = 3782 2 S.F.3 S.F. What is the correct answer? 3800

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Example: You calculate the density of an object with mass of 24.300 grams, and volume of 62.5 ml. How many sig figs in your answer? D=M/V 24.300/62.5 = 0.3888 Correct Sig. Figs. = 0.389

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For addition and subtraction

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Your answer can not contain more decimal places than the least precise measurement.

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Line up the decimal points in the numbers. 2.515 + 1.3 +12.00 =????

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2.515 1.3 + 12.00 15.815 Answer stops here

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Scientific notation

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The number of sig figs comes from the number written before the times sign.

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Examples 3.50 x 10 23 3 S.F. 5.0 x 10 -4 2 S.F. 3 x 10 -4 1 S.F.

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