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Measurement

Uncertainty  A student measures a length of 50.0 cm with a meterstick divided with marks at each millimeter. The uncertainty is about A) 1 cm. A) 1 cm. B) 5 mm. B) 5 mm. C) 0.5 %. C) 0.5 %. D) 0.2 %. D) 0.2 %. E) 0.02. E) 0.02.

How to Measure  Measuring instruments are common. RulerRuler ClockClock SpeedometerSpeedometer ThermometerThermometer Bathroom scaleBathroom scale  All instruments have a scale. Scale can be analog or digitalScale can be analog or digital Instruments can have multiple scalesInstruments can have multiple scales

Analog Scales  Analog scales require interpolation and rounding. Rounding when a value is taken at the nearest tick mark Interpolation when a value is estimated between two adjacent marks

Apparent Shift  A measurement device may not be at the location of the quantity being measured. Change in observation pointChange in observation point Change in resultsChange in results  This can be used to determine the position of the observer relative to the observed point. base angle A angle B

Observing Parallax  Observe an object against the background.  Shift one seat left and observe again.  Subtract to get the parallax shift. 05101520253035404550

Graphs  Both a recording tool and measuring device Keep track of measurements as they are recordedKeep track of measurements as they are recorded Estimate measurements from data on the graphEstimate measurements from data on the graph  Graphs have two scales

Accuracy  The smallest unit on a measuring device sets the accuracy.  In general, a measurement is only as accurate as the smallest unit.  Significant figures are a guide to the accuracy of a measurement.

Significant Figures  Any value is expressed in some number of digits.  The number of digits (without left side zeroes) is the number of significant figures.  With no decimal point, skip right side zeroes. 382 digits, 2 significant figures382 digits, 2 significant figures 5.063 digits, 3 significant figures5.063 digits, 3 significant figures 0.00415 digits, 2 significant figures0.00415 digits, 2 significant figures 7,000.4 digits, 4 significant figures7,000.4 digits, 4 significant figures 2,0004 digits, 1 significant figure2,0004 digits, 1 significant figure

Using Significant Figures  Add or Subtract  Keep the significant figures to decimal place of the least accurate value, rounding as needed. 4.361 + 14.2 = 18.64.361 + 14.2 = 18.6 12000 + 364 = 1200012000 + 364 = 12000  Multiply or Divide  Keep the same number of significant figures as the value with the fewest, rounding as nedeed. 4.361  14.2 = 61.9 12000  364 = 4.4  10 6

Absolute Uncertainty Measure 50.0 cm. Measure 50.0 cm.  There are three significant figures.  The smallest figure suggests an accuracy of 0.1 cm.  This is also equal to 1 mm. The absolute uncertainty has the same type of units as the measurement.

Percent Uncertainty Measure 50.0 cm. Measure 50.0 cm.  Compare 0.1 cm to 50.0 cm.  The ratio is 0.1/50.0 = 0.002.  Multiply by 100 % to get 0.2 %. The percent uncertainty has no units, and is either a pure number or a percent. next

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