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Significant Figures. This module for out-of-class study only. This is not intended for classroom discussion. Significant Figures. Engineers often are doing calculations with numbers based on measurements. Depending on the technique used, the precision of the measurements can vary greatly.

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## Significant Figures

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**Significant Figures**This module for out-of-class study only. This is not intended for classroom discussion.**Significant Figures**• Engineers often are doing calculations with numbers based on measurements. Depending on the technique used, the precision of the measurements can vary greatly. • It is very important that engineers properly signify the precision of the numbers being used and calculated. Significant figures is the method used for this purpose.**Accuracy vs. Precision**Accuracy refers to how closely a measured value agrees with the true value. Ex: A scale to increments of 10 lbs is not very precise, but, if it is well calibrated, it is accurate. Courtesy: http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html**Precision vs. Accuracy**Precisionrefers to the level of resolution of the number. Ex: A scale to increments of tenths of a gram has good precision, however, if it is not well calibrated, it would not be accurate. A scale measures to 0.1 lbs is more precise than one that measures to 1 lbs. Courtesy: College Physics by A. Giambattista, B. Richardson and R. Richardson**Significant Figures and Precision**In engineering and science, a number representing a measurement must indicate the precision to which the measured value is known. The precision of a device is limited by the finest division on the scale. Ex: A meterstick, with millimeter divisions as the smallest divisions, can measure a length to a precise number of millimeters and estimate a fraction of a millimeter between two divisions. Courtesy: College Physics by A. Giambattista, B. Richardson and R. Richardson**Significant Figures**The precisionof a quantity is specified by the correct number of significant figures. Significant figures: All the digits that are measured or known accurately plus the one estimated digit. Ex: d= 12 km (d is 12 km to thenearestkilometer-2 significant fig.) d= 12.0 km (d is 12 km to the nearesttenth of a kilometer-3 significant figures-MORE PRECISE) More significant figures mean greater precision!!! Courtesy: College Physics by A. Giambattista, B. Richardson and R. Richardson**Rules for Identifying Significant Figures**• Nonzero digits are always significant. Ex: 58 - 5 and 8 are significant: 2 significant fig. • Final or ending zeros written to the right of the decimal point are significant. Ex: 58.00 - 5, 8, and zeros are significant: 4 significant fig. • Zeros written on either side of the decimal point for the purpose of spacing the decimal point are not significant. Ex: 0.058 - 5 and 8 are significant - 2 zeros are insignificant: 2 significant fig. • Zeros written between significant figures are significant. Ex: 30.058 - 3, 5, 8 and zeros are significant: 5 significant fig. Courtesy: College Physics by A. Giambattista, B. Richardson and R. Richardson**Exact Numbers**Exact numbers: Numbers known with complete certainty. Exact numbers are often found as conversion factors or as counts of objects. Exact numbers have an infinite number of significant figures. Ex: Conversion factors : 1 foot = 12 inches Counts of objects: 23 students in a class Courtesy: http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/sigfigs4.html**Addition and Subtraction of Significant Figures**When quantities are added or subtracted, the number of decimal places (not significant figures)in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted. Ex: 50.67 J (2 decimal places - 4 significant fig.) 0.1 J (1 decimal place - 1 significant fig.) + 0.9378 J (4 decimal places - 4 significant fig. ) 51.7078 J (4 decimal places- 6 significant fig.) Result: 51.7 J ROUNDING !!! (1 decimal place - 3 sig. fig.) Courtesy: http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm**Multiplication, Division, etc., of Significant Figures**In a calculation involving multiplication, division, trigonometric functions, etc., the number of significant digits in the answer should be equal to the least number of significant digits in any one of the numbers being multiplied, divided etc. Ex: 0.097 m-1 (3 decimal places- 2 significant fig.) X 4.73 m (2 decimal places - 3 significant fig. ) 0.45881 (5 decimal places - 5 significant fig.) Result: 0.46 ROUNDING !!! (2 decimal place- 2 sig. fig.) Courtesy: http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm**Combination of Operations**In a long calculation involving combination of operations, carry as many digits as possible through the entire set of calculations and then round the final result appropriately. DO NOT ROUND THE INTERMEDIATE RESULTS. Ex: (5.01 / 1.235) + 3.000 + (6.35 / 4.0)= 4.05668... + 3.000 + 1.5875=8.64418... The first division should result in 3 significant figures. The last division should result in 2 significant figures. In addition of three numbers, the answer should result in 1 decimal place. Result: 8.6 ROUNDING !!! (1 decimal place - 2 sig. fig.) Courtesy: http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm**Combination of Operations**IF YOU ROUND THE INTERMEDIATE RESULTS: Ex: (5.01 / 1.235) + 3.000 + (6.35 / 4.0)= 4.06 + 3.000 + 1.6=8.66 If first and last division arerounded individually before obtaining the final answer, the result becomes 8.7 which is incorrect. Courtesy:http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/sigfigs4.html**Sample Problems**PLEASE CHECK THE FOLLOWING WEBSITES TO PRACTISE: • http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/sigfigs8.html • http://science.widener.edu/svb/tutorial/sigfigures.html • http://www.lon-capa.org/~mmp/applist/sigfig/sig.htm

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