01 MeasurementReading Ch152

Jan ‘11 Reading a measurement to the correct precision

E1 Measurements

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Dr. Fred Omega Garces

Chemistry 152 Laboratory


Reading measurements to the correct precision

To what precision should a measurement be read? The key is in the graduation or calibration of the measuring device. If the graduation is by tenth or hundredth or thousandth, then the precision is 10% of the graduation. If the graduation is by 2, 0.2, 0.02, then the precision is 25% of the graduation. Read on to see examples.

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Reading Temperature

Temperature in ° C Δ= 1°C, the precision of this thermometer is therefore 0.1°C. The reading of this thermometer is- T = 29.7 + 0.1 °C

Temperature in °F The Fahrenheit scale is a bit more tricky. Here Δ= 2°F, the precision of this thermometer is + 0.5 °F. * The reading of this thermometer is- T = 85.5 + 0.5 °C * 25% of 2 is 0.5

Δ = 1 °C

Δ = 2 °F

In general, when Δ is .1, then the reader can separate the graduation in their mind to 10 equal increments and therefore the precision is to the tenth of the increment (+ 0.01). If however Δ is .2 or in the example above, Δ is 2, then the reader can separate the graduation in their mind to four equal parts. Thus the precision is 25% of the increment (+ 0.5).

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Reading Lengths

To properly read this measurement, note the increment of the calibration. In the ruler above, the increment, Δ, = 0.1 cm. Based on the calibration, the uncertainty or precision of the ruler is +/- 0.01 cm. (In general, the precision or uncertainty of a measurement is generally 10% of the calibration. 10% of Δ (0.1) = 0.01 cm. The reading of the blue bar is therefore, 7.58 + 0.01 cm.

Δ = 0.1 cm

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Reading Mass

When reading a digital scale, all shown digits are significant. The uncertainty is the last digit on the display (the right most digit shown in the scale.) The bathroom scale above changes in increments of 0.1 as the mass is increase therefore, the precision of this scale is + 0.1 lb. The digital scale on the right however changes in increment of 0.05 g. Therefore the precision of the digital pocket scale is + 0.05 g.

Mass reading = 126.4 + 0.1 lb Mass reading = 6.50 + 0.05 g

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Reading Volumes

10-mL Graduated Cylinder Here, Δ = 0.2mL, therefore the precision of this graduated cylinder is 0.05 mL. Therefore the volume reading is- Vol = 6.65 mL + 0.05 mL or 6.60 + 0.05 mL

100-mL Graduated Cylinder Here, Δ = 1mL, therefore the precision of this graduated cylinder is 0.1 mL. Therefore the volume reading is- Vol = 52.5 + 0.1 mL

Δ = .2 mL Δ = 1 mL

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Graphing Techniques

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• Put a 'tle at the top of your graph. The 'tle should indicate the rela'onship you are graphing(e.g., "temperature vs. 'me"). • Label both axes with the quan'ty and unit of the measurement, for example: "'me(seconds)". The independent variable (the one you're controlling) goes on the horizontal x-‐axis; the dependent variable (the one you're watching) goes on the ver'cal y-‐axis. • Label the axes so that the range fills up the page and you don't have much white space on either end.

-‐ Neither axis needs to contain the point (0,0), but they need to be labeled with numbers so you can graph all of your measurements and fill up most of the page with your graphed points. -‐ Start at an appropriate quan'ty just below your lowest value and end at an appropriate quan'ty just above your highest value. -‐ The "appropriate quan''es" should be nice round numbers, depending on the range of values and the available grada'ons of your graph paper. The way you write the numbers on each axis should reflect the precision of your measurements. (For example, if your thermometer reads to the nearest 0.1 °C, and your measurements were from 13.6 to 29.7 °C, then your axis labels could include 10.0, 15.0, 20.0, 25.0,and 30.0 °C, with each equally-‐spaced interval taking up about a quarter of the page.).

Jan ‘11 Reading a measurement to the correct precision 8

• Use a 'ny dot to iden'fy the loca'on of each data point. Use a small circle or other shape to help locate each dot. • Draw a line or curve to show the general trend of your data. If you are graphing what should be a linear rela'onship, use a straightedge (ruler) to draw the best-‐fit straight line through the points.

... Graphing Techniques

-‐The line does not have to touch any of the points, but should have a similar number of points on each side. (The average distance of the points from the line should be about the same on both sides.) -‐  A smooth curve might be a be]er representa'on for some rela'onships. -‐  Never connect the dots with a zigzag line. -‐  The graph is meant to show a trend, not a connect-‐the-‐dots puzzle.


... Graphing Examples


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What to turn in

• You already turned in Prelab Questions. • Complete Data sheet- - Part A, Measurements: Estimates, Measured and Percent difference Average of percent difference for Length, Volume, Temperature & Mass - Part B, Fifty’s: Volume and Relative Error -Part C, Graph: Diameter, Circumference, Ratio C/D Graph of Circumference vs. diameter. Slope is C/D • Complete Postlab questions, turn in next Monday

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01 MeasurementReading Ch152