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# mathhand - Basic Laboratory Mathematics Self-Instructional...

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Basic Laboratory Mathematics Self-Instructional Material SIGNIFICANT FIGURES Those figures in a number that have meaning. The decimal format is used in reporting significant figures. In the laboratory setting, significant figures are determined by the precision and accuracy of a given protocol or piece of equipment. Example: A car speedometer You can't say your speed is 55.467 mph with current speedometers. Car speedometers are accurate + 0.5 mph for analog (dial with needle) meters; therefore a speed of 55 mph is really 54.5 to 55.5 mph. While it is possible to calculate out several places, the information is meaningless if it is beyond the accuracy of the procedure. This is equivalent to false magnification on a microscope where no further resolution is available regardless of the increase in magnification. Rules for recording significant figures: 1. All non-zero digits are significant 2. All zeros between non-zero digits are significant 3. Zeros to the left of implied decimal point may or may not be significant; (one convention uses a bar over the last significant zero, i.e 1200) 4. Zeros to the right of a decimal point and a non-zero digit are significant; they indicate the precision of a number. 5. Zeros to the left of non-zero digit and to right of decimal point are not significant if the value of the number is less than one. Overall the significant figure represents the accuracy and precision of the procedure that produced the number. Example: Test value is reported as 12.6. This implies that the procedure is accurate to the nearest tenth and the actual value is between 12.55 and 12.65. Note that 12.60 implies accuracy to nearest hundredth with the actual value between 12.595 - 12.605. Rounding Off Removing insignificant digits produced as a result of computations. This is done to prevent an implied accuracy due to presence of insignificant digits. 1 MATHHAND.DOC March 27, 2012

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GENERAL RULES FOR ROUNDING OFF 1. If digit dropped is less than 5 then there is no change to preceding digit. 12.64 rounds to 12.6 2. If digit dropped is greater than 5 then the preceding digit is increased by one. 12.66 becomes 12.7 3. If digit dropped is 5 then add 1 if preceding digit is odd, add 0 if preceding digit is even. 3.15 becomes 3.2 3.25 becomes 3.2 Figure Retention When working with figures that have various levels of significant figures, retain only as many significant figures in data as will be necessary to give only one uncertain figure. Example: Reading pipet or buret for titration. The scale is in 0.l ml increments which means you can estimate values between scale divisions (this is called interpolation). Therefore you can report 3.62 ml of acid used; 3.6 is scale reading, .02 is the interpolation. The number 3.62 has only one uncertain figure. Note 3.62 implies that the actual value is between 3.615 & 3.625. This would only be the case if you felt that your estimate was that accurate. If you doubt your ability to be that accurate then report the value as then 3.6.
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mathhand - Basic Laboratory Mathematics Self-Instructional...

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