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Uncertainty in Measurements and Significant Figures

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.

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Uncertainty in Measurements and Significant Figures

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

  2. 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?

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

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

  9. Answer • The measuring capabilities of the device. • 4 sig. figs. • 9.0095  9.010 • 2 sig. figs. • To have the correct number of sig. figs.

  10. References • http://www.google.com • http://invsee.asu.edu/Modules/size&scale/unit2/sigfigadd.gif (Showing the rule of adding with sig. figs.) • http://cdn-write.demandstudios.com/upload//8000/100/10/3/18113.gif (Picture shows how to count the sig. figs.) • http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/index.html (Tutoring on the use of sig. figs.)

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