 # Uncertainty in Measurements and Significant Figures Group 4 Period 1.

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Uncertainty in Measurements and Significant Figures Group 4 Period 1

Uncertainty in Measurements always a certain degree of certainty and uncertainty measurements always have a level of uncertainty Uncertainty depends on the capabilities of the measuring device Review: What does the level of uncertainty depend on?

Rules for Counting Significant Figures include all the certain numbers plus the first uncertain number nonzero integers always count exact numbers have infinite number of sig. figs. (1in.=2.54cm.) exact numbers don’t limit sig. figs in calculations

Continued zeros have 3 classifications leading zeros never count (0.0027  2sf) captive zeros always count (7.032  3sf) trailing zeros count with decimals (100.0  4sf) trailing zeros don’t count without decimals (100  1sf) Review: Which type of zeros are considered sig. figs.? Which are not? Answer: captive and sometimes trailing zeros

Rules for Multiplication and Division of Significant Figures the number of significant figures are limited according to multiplication and division the number of sig. figs. is equal to the number with the least amount of sig. figs. from the problem Review: If 3.2 is multiplied by 2.71, then how many sig. figs. should there be in the answer? Answer: 2 significant figures

Rules of Addition and Subtraction with Significant Figures The number after the decimal in the answer is the same as of a factor with the least decimals. Ex: Review: Solve with correct number of sig. figs. 6.18-3.125=? Answer: 3.055  3.06

Rounding off if the digit following the digit to be rounded is equal or greater than 5, then the preceding digit is increasing by 1 if the digit following the digit to be round is less than 5, then the preceding digit stays the same necessary to round to have correct number of significant figures carry digits to the final result then round Review: If the number after the digit is greater than 5, what happens to the number to be rounded? Answer: the number to be rounded increases by one

Quiz 1) What does the level of uncertainty depend on? 2) 0.0670  How many sig. figs.? 3) (1.408 + 9.273) – 1.6715 = ? 4) 3.2 x 2.17  How many sig. figs. are in the answer? 5) Why is it necessary to round in chemistry?

Answer 1) The measuring capabilities of the device. 2) 4 sig. figs. 3) 9.0095  9.010 4) 2 sig. figs. 5) To have the correct number of sig. figs.

References http://www.google.com http://invsee.asu.edu/Modules/size&scale/uni t2/sigfigadd.gif (Showing the rule of adding with sig. figs.) http://invsee.asu.edu/Modules/size&scale/uni t2/sigfigadd.gif http://cdn- write.demandstudios.com/upload//8000/100/ 10/3/18113.gif (Picture shows how to count the sig. figs.) http://cdn- write.demandstudios.com/upload//8000/100/ 10/3/18113.gif http://www.chem.sc.edu/faculty/morgan/reso urces/sigfigs/index.html (Tutoring on the use of sig. figs.) http://www.chem.sc.edu/faculty/morgan/reso urces/sigfigs/index.html

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