Measurement: Uncertainty, Precision, Accuracy, and Error

Numbers from measurements are different compared to other numbers.

· Measurements represent an action by someone with some measuring instrument.

· No measuring instrument is completely accurate.

· Measurements have built-in uncertainty or error

Error affects:

· Accuracy (how close to the true value) and

· Precision (the closeness of repeat measurements to each other).

Whenever a measurement is made, an estimate is part of the number.

The uncertainty (estimate) in the measurement needs to be communicated.

Uncertainty:

The level of uncertainty of a measurement should always be expressed in the numbers recorded.

· The use of significant figures in a measurement expresses the level of uncertainty.

· The number of digits that are known for sure, plus the estimated digit – the last digit in the number – expresses the level of uncertainty.

Precision versus Accuracy:

Look at each target below and decide whether the situation is accurate, precise, both, or neither:

(Note:  it is “accepted” that the bull’s eye is the place everyone aims for.)

Error:

Comparing the measured value to the true value – expressing error as a percent

· % error   =  x 100

Measurement:

Measurement practice: Animation of measurement using rulers and graduated cylinders (answer/instant grading)

http://chemsite.lsrhs.net/measurement/images/measurement%20tutorial.swf

Supplement:

1.  Graduated Cylinder:

• Measurement-4
• Measurement-5

2.  Thermometer

• Measurement-1: A – D only

Experiment 2 A&B (20 pts)

Introduction to accuracy of measurement

• Three trials of mpg
• Difference: trial values versus EPA accepted values

Difference in numbers tells you:

• Magnitude of difference
• Direction of difference
• Units of measure

Density: a ratio of weight over volume

Experiment 2A: Density of a Liquid

Experiment 2B: Density of a solid (includes an unknown).  Attempt direct measure?

A measurement always consists of two parts:

• a number
• a unit

Measurements always have error or uncertainty

Scientific Notation

• Rules: SciNotation.pdf
• Practice: http://janus.astro.umd.edu/astro/scinote/

Measurement

• Practice: Measurement animation – rulers and grad cylinders

http://chemsite.lsrhs.net/measurement/images/measurement%20tutorial.swf

http://www.carlton.srsd119.ca/chemical/Sigfigs/contents.htm

Significant Figures:

• Practice: Sig. Fig. animation http://chemsite.lsrhs.net/measurement/countingsigdigflash.html
• http://www.carlton.srsd119.ca/chemical/Sigfigs/contents.htm