CHEM1000_Significant Figures

CHEM1000_Significant Figures - Significant Figures;...

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Significant Figures; Round-Off Errors; Conversion Factor Method Particularly in the first term of CHEM 1000, there is a considerable emphasis on working problems and doing calculations; they form the basis of the quizzes and examinations. Many students from high school have encountered the following frustration. You work a problem and get an answer of 45.2; your friend's answer is 45; another student got 45.1936. Sometimes students and even teachers say "It doesn't really matter; so long as you understand it . . . " Nonsense! It does matter! If the problem is based on measured experimental data, there is only one right answer. Otherwise, all we are doing is sweeping the mess under the carpet and trying to pretend it doesn't exist. Intellectually, that is very unsatisfying. In the little illustration above, one answer is correct and two are wrong. If these appeared on one of our quizzes or exams, two of the students would receive a deduction of ½ or 1 mark for "wrong sig. figs." One of our objectives in CHEM 1000 is to educate experimental scientists to handle data properly. Put out a little effort right now and it will pay big dividends for the rest of your scientific life. Very soon it will become second nature to use significant figures correctly. In practice, the correct handling of sig. figs. can be taken care of by a few simple rough-and- ready Rules . 1. Put all the data into the calculation using all the digits you've got. Train yourself to do this even when it is a rough "first attempt". 2. When you multiply and/or divide numbers, it is the number with the fewest sig. figs. which controls the answer. 3. When you add and/or subtract numbers, it is the number with the fewest decimal places which controls the answer. Number of Significant Figures Let us first be clear on the number of sig. figs. A few examples will suffice (number of sig. figs. in brackets). 4.168 (4). 416.8 (4). 2.0000 (5). 2×10 6 (1). If it was accurate to 3 sig. figs. you would write it as 2.00×10 6 ; the power of 10 just shifts the decimal place but does not affect the accuracy. 0.000359 (3); it is the same as 3.59×10 4 with a shift of the decimal point. "The tunnel is 200 m long." Bad! Ambiguous! It isn't clear if the tunnel is 2×10 2 (1), 2.0×10 2 (2) or 2.00×10 2 (3) m long. It may be necessary to use ×10 1 ; e.g. 60 to 1 sig. fig. is expressed by 6×10 1 . Round-Off Errors One of the advantages of using sig. figs. properly is that you avoid round-off errors. Everyone is familiar with the procedure for rounding off: if the last digit is 0 to 4, don't change the previous digit; if it is 5 to 9, raise the previous digit by 1. For example, if the number of sig. figs. is (2), 67.3 or 67.0 round off to 67, but 67.5 or 67.9 round off to 68. The following little problem shows how indiscriminate rounding off can introduce errors.
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CHEM1000_Significant Figures - Significant Figures;...

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