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Measurement Conversions Accuracy and Precision Sig. Fig.’s and more

Measurement Conversions Accuracy and Precision Sig. Fig.’s and more. Dimension - the kind of physical quantity being measured Examples: length, mass, time, volume, and so on Each dimension is measured in specific units. meters, kilograms, seconds, liters, and so on

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Measurement Conversions Accuracy and Precision Sig. Fig.’s and more

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  1. MeasurementConversionsAccuracy and PrecisionSig. Fig.’sand more

  2. Dimension - the kind of physical quantity being measured • Examples: length, mass, time, volume, and so on • Each dimension is measured in specific units. • meters, kilograms, seconds, liters, and so on • Derived units are combinations of other units. • m/s, kg/m3, and many others • Scientists use the SI system of measurement. MEASUREMENT

  3. SI Standards

  4. Important Metric Prefixes

  5. Build a conversion factor from the previous table. Set it up so that units cancel properly. • Example - Convert 2.5 kg into g. • Build the conversion factor: • This conversion factor is equivalent to 1. • 103 g is equal to 1 kg • Multiply by the conversion factor. The units of kg cancel and the answer is 2500 g. • Try converting • .025 g into mg • .22 km into cm Converting Units

  6. If a Ms. Bjork has a mass of • 60,000,000 mg, what is her mass in grams and in kilograms? • Answer: 60 000 g or 60 kg Practice Problem

  7. ACCURACY AND PRECISION • Precision is the degree of exactness for a measurement. • It is a property of the instrument used. • The length of the pencil can be estimated to tenths of centimeters. • Accuracy is how close the measurement is to the correct value.

  8. Error • Associated with a measurement • Cannot be exactly determined (otherwise you could make a more accurate measurement) • Not a “blunder”, human errors are not experimental errors • Uncertainty in a measurement which nothing can be done about

  9. RANDOM ERROR Two main classifications of error SYSTEMATIC ERROR Shift all measurements (systematically) Calibration issues Improper use of equipment Failure to account for some effect Systematic error reduces accuracy Fluctuate from measurement to measurement (distributed around some mean value) Lack of sensitivity (Of instrument or observer) Noise (extraneous disturbances) May occur due to statistical processes (roll of the dice) Random error reduces precision

  10. Errors in Measurement Instrument error Instrument error is caused by using measurement instruments that are flawed in some way. Instruments generally have stated accuracies such as “accurate to within 1%.” Method error Method error is caused by poor techniques (see picture below).

  11. Significant Figures • Non zero digits are significant • Zero’s b/w non zero digits are significant • Zero’s to the left of the first non zero digit are not significant (think scientific notation) • Zero’s to the right of a decimal point are significant • For number w/out a decimal point, trailing zero’s are not significant

  12. Significant Figures: Calculations

  13. What do you think? What different ways can you organize data so that it can be analyzed for the purpose of making testable predictions?

  14. Tables This table organizes data for two falling balls (golf and tennis) that were dropped in a vacuum. (This is shown in Figure 13 in your book). Can you see patterns in the data?

  15. Graphs Data from the previous table is graphed. A smooth curve connects the data points. This allows predictions for points between data points such as t = 0.220 s. The graph could also be extended. This allows predictions for points beyond 0.400 s.

  16. Equations Show relationships between variables Directly proportional Inversely proportional Inverse, square relationships Describe the model in mathematical terms The equation for the previous graph can be shown as y = (4.9)t2. Allow you to solve for unknown quantities

  17. Dimensional Analysis Dimensions can be treated as algebraic quantities. They must be the same on each side of the equality. Using the equation y = (4.9)t2 , what dimensions must the 4.9 have in order to be consistent? Answer: length/time2 (because y is a length and t is a time) In SI units, it would be 4.9 m/s2 . Always use and check units for consistency.

  18. Order of magnitude Rounds to the nearest power of 10 The number 65 has an order of magnitude of 102 because it is closer to 102 than to 101 What is the order of magnitude for 4200, 0.052 and 6.2 x 1023? Answers: 103, 10-1 , and 1024 Allows you to get approximate answers for calculations

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