Significant Digits and Uncertainty in Measurement Lab_ AP vers 2.0

Name______

Lab Partners______

Block #______

Goals: To obtain precise measurements using significant digits and uncertainty techniques.

To apply rules of Significant digits and Worst case uncertainty techniques to calculations.

To compare the 3 methods (significant digits and uncertainty worst case)

To realize how larger sample size can provide better precision (page thickness portion of lab)

To consciously attempt to maximize the group effort and equity.

Procedure: Described by your physics teacher at the outset of the lab

References: Significant digits rules in notes and textbook

Worst case uncertainty sample calculations

Caliper practice sheets

Data table I : Ruler measurement using “worst case” uncertainty technique

Volume of
The block
With Ruler / Measurement / Uncertainty / Uncertainty
Percentage
Length
Width
Height
Un-rounded Volume
(limit to 6 digits) / Un-rounded Worst case uncertainty / Volume stated with uncertainty correctly
(rounded correctly**)
Volume stated w/ rounded uncertainity using added percentages

**refer to notes/handout to review how to round uncertainty and volume correctly

Data Table II

Volume of Block - using ruler Significant Digits
Length
Width
Height
Volume un-rounded / Volume Rounded to the Correct # of Sig Dig's

Data Table III: Measure the same block with calipers, estimate uncertainty, then use the “worst case” technique to determine the uncertainty in volume.

Volume of
The block
WithCalipers / Measurement / Uncertainty / Uncertainty
Percentage
Length
Width
Height
Un-rounded Volume
(limit to 6 digits) / Un-rounded Worst case uncertainty / Volume stated with uncertainty correctly
(rounded correctly**)
Volume stated with rounded uncertainty using added percentages

Data Table IV

Volume of Block - using calipers Significant Digits
Length
Width
Height
Volume un-rounded / Volume Rounded to the Correct # of Sig Dig's

Part 2 : Measuring page thickness with calipers:

Construct a data table** that shows data needed to determine the thickness of a single textbook page. Use data samples of 50, 100, and 200 pages. Estimate uncertainty in your measurements and discuss how that uncertainty transfers to the "per page thickness" data. Follow the same rounding rules: Uncertainties should be rounded to 1 significant digit (unless they begin with the digit 1; in this case, round to 2 significant digits) , then round your calculated value to the same decimal place as your uncertainty.

*Focus on how the sample size affects the per page uncertainty.

Data to include total measured thickness, uncertainty estimate of total sample thickness, calculated per page thickness, calculated per page uncertainty.

Sample Data Table

# of sheets / Total Thickness
(units) / Uncertainty in Total
Thickness (units) / Calculated per page thickness (units) / Uncertainty per page
(units)
50
100
200

Questions: (please answer neatly on loose leaf or typed up)

  1. Explain how the ruler and caliper illustrated different precision levels in measuring.
  1. Look at the data and compare the method of significant digits to uncertainty. What are the "pro's and con's" of each method.
  1. Take note of the difference in the measurement of volume between the calipers and rulers. For all groups with valid data, the volume measured with the calipers will always be larger than the volume measured with the ruler. Why is this? Wait, it has to do with the block…and the different way rulers and calipers measure the block…..
  1. Which way of communicating uncertainty do you prefer; S.D. or worst case uncertainty? Why?
  2. Of the 2 ways to handle uncertainty: Worst case and added percentages, which do you prefer and why?
  3. How did the sample size (in the page part) affect the "per page" uncertainty?
  4. Explain why this is so (# 6).
  5. How well was the work by your group shared? Think of something that you can do next time to improve the way your lab group works.
  6. Do some “lightning research” on your browser on precision and accuracy in science labs and read through. Comment on some of things you come across- be ready to discuss with class. ( spend ~ 10 minutes on browser; ~ 10 minutes typing up summary of relevant ideas you encountered. No citations requested for this.

Lab Report:

Download the Word version of this and type in your final values and answers. Be sure to proofread before printing out.