2.5 Reading Measurements and Experimental Uncertainty (Part 1)

2.5 Part 1 Learning Outcomes Learn how to find and report the uncertainty associated with each measurement Determine if a measurement is accurate and/or precise Determine certain and uncertain digits in a measurement Determining experimental uncertainty

Part 1 Vocabulary Counting Exact or Definite number Uncertainty Significant figure Accurate Precise Certain verses uncertain digits Experimental uncertainty

2.5 Part 1 Summary Notes (Reading Measurements and Experimental Uncertainty): Sample Question 1: Write the following measurement and its uncertainties in the correct form- a balance gives the measurement of 51.32g with an uncertainty of 0.01g 51.32 +/- 0.01g Sample Question 2: The correct volume of a metal is 18.72 cm3 A several readings of 17.521 would be precise but NOT accurate A reading of 18 would be accurate but NOT precise

Summary Notes: counting a small # of objects = exact or definite measuring mass, time, volume, length = measured and are never exact All measurements have uncertainty associated with them Significant figure is a measured or MEANINGFUL digit (see SWB page 27 for examples)

Accurate and Precise: Accurate= measure that is close to the correct or accepted value Precise= reproducible measurement, more significant digits/more decimal places

Can you hit the bull's-eye? Three targets with three arrows each to shoot. How do they compare? Both accurate and precise Precise but not accurate Neither accurate nor precise

Can something be precise but not accurate (or vice versa)? YES!!! if precise, but not accurate there is a systematic error or bias Ex. you get the same wrong answer over and over if accurate but not precise, experimenter is being inconsistent

For example: Assume the CORRECT measurement of a pencil is 27.3200 cm.

LOTS of Sig Figs

Uncertainty (not just a feeling)

We would write this as…. 42.6 +/- 0.1 mL

Another Example: What number would this be?

More Examples: 6.214 6.372

Uncertainty in Measurements: The uncertainty is always in the last digit (the one that was estimated) This can be expressed as part of the number Ex. 42.7 + 0.1mL uncertainty term

Uncertainty in Measurements: The uncertainty is always in the last digit (the one that was estimated) This can be expressed as part of the number Ex. 42.7 + 0.1mL  Range = 42.6 to 42.8mL

Assume that a measured temperature is 39 Assume that a measured temperature is 39.6ºC and the uncertainty is ± 0.1ºC. We write it as: The RANGE for the above measurement is from 39.5 – 39.7ºC.

Practice task(s) to learn these new skills 1. Exercise 43-47 page 29 (Accurate and precise, certain digits and measurement/counting) 2. Exercise #48 page 32, #49 page 33 and #50 page 34 (practice reading scales) 3. Exercise # 51 and #52 page 35 and finally Exercise # 53 and 54 page 36