Precision

1
Precision Uncertainties
2
Significant Digits

• How many digits do I use?
• Unless there is a digital display, always measure
  to one spot beyond the smallest unit of CERTAIN
  measurement of the tool.

3
Precision in Measurements
Measurements must be reported to the correct
number of digits.
4
Determine the RULE for measuring with the
correct number of digits
Remember measure to one spot beyond the smallest
unit of CERTAIN measurement of the tool.
5
Measurement and Uncertainties
Random error Systematic error
It is a random error if you get lots of slightly different readings when making a measurement It is a systematic error if there is something wrong with the equipment of method when taking a measurement
You can reduce the error by repeating the measurement Error CAN NOT be reduced by repeating the measurement
It is easy to spot random error when collecting data by the variance of the readings Not easy to spot right away but it may become evident when a linear graph that should cross the origin has a relevant y-intercept
6
Precision vs Accuracy

• An ACCURATE experiment is one that has small
  systematic error, whereas a PRECISE experiment is
  one that has a small random error
• An experiment may have great precision but be
  inaccurate

7
Uncertainty
measurement best estimate uncertainty

• Every measurement has an uncertainty
• The lower the accuracy and precision of a
  measurement instrument are, the larger the
  measurement uncertainty is.
• The numerical value of a uncertainty value
  tells you the range of the result. For example a
  result reported as 1.23 0.05 means that the
  experimenter has some degree of confidence that
  the true value falls in between 1.18 and 1.28
• measurement best estimate uncertainty

8
To determine uncertaintyFind the smallest
increment of measurement on your measurement
device and divide it by two
This line would be measured as 4.50 cm /- 0.05
cm
9
How many digits?Uncertainty?
10
How many digits?Uncertainty?
11
How many digits?Uncertainty?
12
Whats the Uncertainty?