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Unformatted text preview: Units and Significant Figures Units and Significant Figures Learning Objectives Learning What are engineering units and notations? How many significant figures should you use? Systems of Units Systems), formerly MKS uI nternational Systemof Units (SI
Fundamental Fundamental Quantity Quantity Length Mass Time Electric Current Temperature Luminous Luminous Intensity Intensity Unit Meter Kilogram Second Amperes Kelvin Candela Abbreviation m Kg s A K cd Systems of Units Systems Engineers tend to use powers divisible by Engineers 3 (engineering notation)
• Standard prefixes:
micro milli kilo mega µ m k M 106 103 103 106 109 giga G Systems of Units Systems 5 Suppose a calculation results in a value of 105 in amps. What is the value in engineering notation? amps. Engineers Use Units! Engineers The current in the resistor is 5 Five what? Amps, mA, µA?
Any num ric quantity m haveunits. e ust Without units theanswe is incom te r ple . Significant figures Significant 2000 > 2 x 103 one significant figure one
• Lies between 1 x 103 2 x 103 10 3 x 103 10 2000 > 2.0 x 103 two significant figures two
• Lies between 1.9 x 103 2.0 x 103 2.0 2.1 x 103 2.1 Precision Precision There is a relationship between the There number of significant figures and the implied precision implied
Number Absolute Absolute Error Error ±5 ± 0.5 ± 0.05 ± 0.005 Precision (%) 10 1 0.1 0.01 Number of Number significant Figures Figures 1 2 3 4 50 or 50. 52 or 52. 52.4 52.37 General RulesSignificant Figures General Zeros within a number are always Zeros significant significant
• 4308 and 40.05 each have 4 significant figures Zeros that do nothing but set the decimal Zeros point are not significant point
• 470,000 has two significant figures • 0.0081 has two significant figures Trailing zeros after the decimal point are Trailing significant significant
• 4.00 has 3 significant figures • 151.0 has 4 significant figures General RulesSignificant Figures General Addition and subtraction:
• The accuracy of the final answer can be no The greater than the least accurate value greater • The answer can contain no more decimal The places than the least accurate value places • Example: 150.0 Ω (1 number after decimal 150.0 point) point) + 0.507 Ω (3 numbers after decimal point) point) 150.507 rounds to 150.5 Ω 150.507 General RulesSignificant Figures General Multiplication and Division
• The final answer to a multiplication or division The problem can contain no more significant figures no than the least accurate value* than • Example: 15.03 ( 4.87 ) = 36.837 W 1.987 • Round to 36.8 W
An alte rnativerulein which onem significant figurethan thestandard ruleis use has be n shown ore d e t o besom what m accurate S ere re 3. e ore . e fe nce
* EE302 and Significant Figures EE302 Use the number of significant figures Use specified in any problem. specified If none is specified, you should use three If significant figures in final answers significant For lab measurements, three significant For figures is the maximum to be expected figures You will be expected to use the appropriate You significant figures on HW, lab reports, and exams exams Other Rules Other For decimal fractions less than one, For explicitly write a leading zero for decimal fractions to emphasize the placement of the decimal point the Example:
• Incorrect: .28 • Correct: 0.28 ...
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 Spring '09
 MCCANN

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