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Measurements and Their Uncertainty

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Significant Figures in Calculations

Significant Figures

in Addition and Subtraction

Calculations

3.1

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Measurements and Their Uncertainty

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3.1 Significant Figures in Calculations***Rules for determining number of SF in final answer when Adding or Subtracting

•do the mathematical operation

•the value with the least number of decimal places in the original data determines the place of the last sig fig in the answer .

•Round appropriately to report final answer

•Convert to scientific notation if needed

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Measurements and Their Uncertainty

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C. Significant Figures

67.9 mL

28.29 g

63.75 mL

+ 4.1 mL

32.587 g

- 4.30 g

67.85 mL

28.287

Ex. 1

Try this:

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SAMPLE PROBLEM

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Always re-write to line up the decimal 12.52 349.0 8.24 369.76 do the math

ANS: 369.8 m just for fun…write in scientific notation 3.698 x 102 m

Least number of decimal places

Round correctly

****SigFigs in standard or scientific must always be the same but decimal places do not have to be the same!!!!!******

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Measurements and Their Uncertainty

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C. Significant Figures

1150 g

924 g

+ 230 g

1.15 x 103 g

If values you are adding or subtracting, don’t have decimal points, the least accurate number determines the number of SF in the final answer

1154 g

Ex. 2

Notice, rules for adding sf determined: 3 sig figs and no decimal pointBut, rules for converting from standard to SN determined: just keep total number of SF the same and do not worry about decimal places!

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SAMPLE PROBLEM

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write each number so the exponents are identicalre-write to line up the decimaldo the mathematical operationround to correct number of sig figsput final answer in correct scientific notation

Example: 3.75 x 10-5 m + 7.00 x 10-5 m 3.75 x 10-5 + 7.00 x 10-5

10.75 x 10-5 round to the least number of decimal places 10.75 x 10-5

Write in proper scientific notation (b/c original given in sn) ANS: 1.075 x 10-5 m (notice different number of decimal places!!!)

Adding and Subtracting w/ Scientific Notation

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SAMPLE PROBLEM

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Try this: 3.6 x 10-5 m + 6.5 x 10-4 m

Convert to the same exponent and re-write with decimals lined up . 36 x 10-4 3.6 x 10-5

+ 6. 5 x 10-4 + 65. x 10-5

6. 86 x 10-4 68.6 x 10-5

6.9 x 10-4 m or 69 x 10-5

ans: 6.9 x 10-4 m

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SAMPLE PROBLEM

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PRACTICE PROBLEMSin packet