#### Transcript Uncertainty and error in measurement

MEASUREMENTS 1 MEASUREMENT AND DATA PROCESSING 1 SIGNIFICANT DIGITS PRECISION & ACCURACY http://web.me.com/dbyrum/Ris/Resources/page29/files/ErrorAnalysis.pdf http://www.wellesley.edu/Chemistry/Chem105manual/Appendices/uncertainty_analysis .html Imp: http://chemwiki.ucdavis.edu/Analytical_Chemistry/Quantifying_Nature/Uncertainties_in_ Measurements TYPES OF OBSERVATIONS AND MEASUREMENTS We make QUALITATIVE observations of reactions — changes in color and physical state. We also make QUANTITATIVE MEASUREMENTS, which involve numbers. SIGNIFICANT DIGITS http://chemsite.lsrhs.net/measurement/sig_fi g.html RULES Rules for deciding the number of significant figures in a measured quantity: (1) All nonzero digits are significant: 1.234 g has 4 significant figures (2) Zeroes between nonzero digits are significant: 1002 kg has 4 significant figures (3) Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: (placeholders are not significant) 0.012 g has 2 significant figures. (4) Trailing zeroes that are also to the right of a decimal point in a number are significant: 0.0230 mL has 3 significant figures, 0.20 g has 2 significant figures (5) When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 190 miles may be 2 or 3 significant figures, 50,600 calories may be 3, 4, or 5 significant figures. Trayling zeros: 190000 = 2 s.d ( could be up to 6) In the last example, where the number 19000 has an ambiguous number of significant digits, scientific notation will clear up this problem. 1.90 x 104= 19000 and has 3 significant digits. 1.9 x 104= 19000 and has 2 significant digits. 1.9000 x 104= 19000 and has 5 significant digits. PROBLEMS: 1) 7000 2) 450.0 3) 350 4) 0.006200 7) 565.05 8) 5500 9) 74.00 10) 7040.0 IB PROBLEM: RULES FOR MATHEMATICAL OPERATIONS: In carrying out calculations, the general rule is that the accuracy of a calculated result is limited by the least accurate measurement involved in the calculation. I. In addition and subtraction, the result is rounded off so that it has the same number of decimal places as the measurement having the fewest decimal places. For example, 100 (3 s.f) + 23.643 (5 s.f) = 123.643, which should be rounded to 124 (3 s.f). II. In multiplication and division, the result should be rounded off so as to have the same number of significant figures as in the component with the least number of significant figures. When there are series of calculations, do not round off until the end. For example, 3.0 (2 s.f ) × 12.60 (4 s.f) = 37.8000 which should be rounded off to 38 (2 s.f). PROBLEMS: http://www.fordhamprep.org/gcurran/sho/sho /lessons/lesson23.htm PRECISION AND ACCURACY IN MEASUREMENTS Precision How reproducible are measurements? Accuracy How close are the measurements to the true value. 14 PRECISION&ACCURACY Accuracy Accuracy, measures the agreement between a measurement and the accepted standard value. Refers to how close a measurement is to the real value. If a balance consistently gives a value of 3.64 g on repeated measurements, its precision is good. However, if the actual mass is 3.75 g, its accuracy is poor! Precision Precision measures the agreement between results of repeated measurements. Refers to reproducibility or how close the measurements are to each other. A balance that can read mass to 0.0001 grams should be more precise than one that reads mass to 0.1 grams. PRECISION OF A MEASUREMENT Measurement ≈ 26.13 cm The last digit is an estimate. The precision is limited by the instrument. Science, Measurement, Uncertainty and Error 17 IB PROBLEM The goal in the Chemistry laboratory is to obtain reliable results while realizing that there are errors inherent in any laboratory technique. http://www.savitapall.com/scientific_measuremen t/notes/measurement%20and%20data%20proce ssing.pdf http://teachers.rickards.leon.k12.fl.us/Teacher s/mcdonald/Senior%20IBAP%20Webpages/No tes/11.%20Measurement%20and%20Data%2 0Processing/Measurement%20and%20IA.%20 DP,%20CE.htm HTTP://WWW.DARTMOUTH.EDU/~CHEMLAB/INFO/RESOURCES/UNCERTAIN.HTML http://www.wellesley.edu/Chemistry/Chem105 manual/Appendices/uncertainty_analysis.html