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Uncertainty and Error in Measurement

Uncertainty and Error in Measurement. Let’s Think…. You measure the temperature of a glass of water 10 times, using 10 different thermometers. Results in Celsius : 19.9, 20.3, 20.2, 20.0, 20.0, 20.1, 19.9, 20.3, 19.9, 20.2 How would you accurately report the final temperature?.

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Uncertainty and Error in Measurement

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  1. Uncertainty and Error in Measurement

  2. Let’s Think… You measure the temperature of a glass of water 10 times, using 10 different thermometers. Results in Celsius : 19.9, 20.3, 20.2, 20.0, 20.0, 20.1, 19.9, 20.3, 19.9, 20.2 How would you accurately report the final temperature?

  3. Let’s Think… Answer the following questions related to the data collected. • Is it reasonable to assume that the actual temperature is about 20ᵒC? Why or why not? 2. If not, what would the reasonable result be? Actual result…. 20.08  20.1  20.1 +/- 0.2 ᵒC This result is both reasonable And precise!

  4. Precision • Refers to how close several experimental measurements of the same quantity are to each other • In previous example: • If one student took all the temp. readings, they would be said to be repeatable, whereas if several students had taken the readings they would be said to be reproducible.

  5. Accuracy • How close a precise reading is to the true reading (literature value) • If all thermometers are reading 20ᵒC when the true value of the temp is 19ᵒC, then they are giving precise but inaccurate readings • This is due to systematic errors • Due to the apparatus itself, or due to the way in which the readings are taken

  6. Systematic error

  7. Random Error • Occur if there is an equal probability of the reading being high or low from one measurement to the next • Might include variations in the volume of the glassware due to temp fluctuations, or the decision on ten an indicator changes color during and acid base titration

  8. Significant Figures • Significant figures are critical when reporting scientific data because they give the reader an idea of how well you could actually measure/report your data.

  9. Significant Figures Four Main Rules • All non zero numbers are ALWAYS significant ex) 125, 34, 971 • Leading zeros are NOT significant. They indicate the position of the decimal ex) 0.0025 , 0.01, 0.00347

  10. 3) Zeros that are sandwiched between non zero numbers are ALWAYS significant. ex) 103, 4009, 12.05 4) Trailing zeros at the right end of a number are significant ONLY if the number contains a decimal point ex) 100, 20 (1 sig fig) ex) 100. , 20.0 (three sig figs)

  11. Practice...

  12. Addition and Subtraction • When adding or subtracting, it is the number of decimal places that is important. • When using a balance that measures +/-0.01 g, the answer can be quoted to two decimal places, which may increase or decrease the number of significant figures.

  13. Addition and Subtraction • Example: 7.10 g + 3.10 g = 10.20 g 3 sig figs 3 sig figs 4 sig figs 22.36 g + 5.16 g = 7.20 g 4 sig figs 4 sig figs 3 sig figs

  14. Multiplication and Division • When multiplying or dividing, it is the number of significant figures that is important. • The number with the fewest significant figures used in the calculation determines how many significant figures should be used when writing the answer

  15. Multiplication and Division Examples 4.56 x 1.4 = 6.38  6.4 3 sig figs 2 sig figs 3 sig figs 2 sig figs 3.217 x 2.64 = 8.49288  8.49 4 sig figs 3 sig figs 6 sig figs 3 sig figs

  16. Practice… • 1.20 + 2.35 = 3.6 • 32.0 – 27.0 = 5.0 • (6.3 + 2.2 ) – 3.9 = 4.6 • 6.2 x 7 = 43.4  40 • 46.12 / 13 = 3.54  3.5 • (2.3 x 4.00) / 1.7 = 5.41

  17. Uncertainties • It the degree of tolerance is not stated on an apparatus, you will have to estimate • Degree of tolerance, is where the manufacturer lists the uncertainty of the apparatus

  18. If you are making a single measurement with a piece of apparatus, the absolute uncertainty & the percentage uncertainty can both be easily stated. • For example, Consider measuring 25.0 cm3 with a 25 cm3 pipette that measures to +/- 0.1 cm3 . The absolute uncertainty is 0.1 cm3 and the percentage uncertainty is equal to… 0.1 / 25.0 x 100 = 0.4%

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