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Measurement

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. B) 5 mm. C) 0.5 %. D) 0.2 %. E) 0.02. How to Measure. Measuring instruments are common. Ruler Clock Speedometer Thermometer

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Measurement

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  1. Measurement

  2. 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. • B) 5 mm. • C) 0.5 %. • D) 0.2 %. • E) 0.02.

  3. How to Measure • Measuring instruments are common. • Ruler • Clock • Speedometer • Thermometer • Bathroom scale • All instruments have a scale. • Scale can be analog or digital • Instruments can have multiple scales

  4. 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

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

  6. 0 5 10 15 20 25 30 35 40 45 50 Observing Parallax • Observe an object against the background. • Shift one seat left and observe again. • Subtract to get the parallax shift.

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

  8. 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.

  9. 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. • 38 2 digits, 2 significant figures • 5.06 3 digits, 3 significant figures • 0.0041 5 digits, 2 significant figures • 7,000. 4 digits, 4 significant figures • 2,000 4 digits, 1 significant figure

  10. Add or Subtract Keep the significant figures to decimal place of the least accurate value, rounding as needed. 4.361 + 14.2 = 18.6 12000 + 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  106 Using Significant Figures

  11. 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. Absolute Uncertainty The absolute uncertainty has the same type of units as the measurement.

  12. 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 %. Percent Uncertainty The percent uncertainty has no units, and is either a pure number or a percent. next

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