QUESTION: How should the result of the following calculation be reported? 0.0072 + (0.0050)(39.0) A. 0.20, B. 0.21, C. 0.202, D. 0.2022.

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Presentation transcript:

QUESTION: How should the result of the following calculation be reported? 0.0072 + (0.0050)(39.0) A. 0.20, B. 0.21, C. 0.202, D. 0.2022 Step 1. Multiply: (0.0050) (39.0) = 0.195, two sigfigs only, but keep extra digit to avoid round-off errors Step 2. Add: 0.0072 + 0.195 SCRIPT 1A-4-5 How should the result of the following calculation be reported? 0.0072 plus 0.0050 times 39.0 0.20… 0.21… 0.202… Or 0.2022 CLICK Whenever we have to do a series of calculations involving significant figures, it is best to keep an extra digit in the intermediate results in order to avoid a build up of round off errors. In the case shown here, when we multiply 0.0050 by 39.0, we get an intermediate result of 0.195, which should be rounded off to two significant digits, since there are two significant digits in 0.0050 and three significant digits in 39.0. The rule for multiplication and division says that we should round off to same number of significant figures as the term with the fewer number of significant figures. However, we keep an extra digit when we carry this intermediate result over to another calculation. In the second step, we apply the rule for addition and subtraction. We keep in mind that the last significant digit in 0.195 is actually in the second place after the decimal point, not the third. The last significant digit in 0.0062 is the fourth place after the decimal point. Therefore, the 0.195 term has a larger uncertainty. The last significant digit of our final answer should be in the second decimal place. PAUSE 2 seconds END RECORDING 0.2022  0.20

Video ID: 1A-4-5 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08