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Understanding Measurement Uncertainty and Significant Figures

Learn about measurement uncertainty, significant figures, and techniques for accurate measurements. Explore analog scales, observing parallax, using graphs, and calculating accuracy. Understand how to manage significant figures in calculations.

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Understanding Measurement Uncertainty and Significant Figures

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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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