Experiment 0 – Exploring the Instruments and ORIGIN
1
Example Question
Question:
The unrounded value of length, x, is 2,346.67cm.
The unrounded uncertainty,
!
x is
23cm.
What is the rounded value of x with rounded uncertainty?
Answer:
Since the most significant (leftmost) digit of
!
x is not a ‘1’ the first digit is rounded.
Thus, the rounded uncertainty is 20cm.
Since the last significant digit of the
uncertainty is the tens place then the value of x must be rounded to this place as well.
So x
=
2,350
±
20
cm.
You could also use Taylor’s standard for rounding to the second digit when the most
significant digit is ‘2’.
The answer would then be x
=
2,347
±
23
cm.
Experiment 0  Exploring the Instruments and ORIGIN
Introduction
The goal of this laboratory is to become familiar with some of the tools and techniques you will be
using throughout the quarter.
Many of these tools will be used for the next several labs (e.g. the
oscilloscope), and others you will use during every lab (e.g. ORIGIN software).
If you pay close
attention to the functions of the various devices you will be examining this week, your future
experiments may proceed more smoothly.
1
Data Analysis
1.1 Significant Figures / Rounding
Proper analysis of data requires that you are familiar with and use significant figures.
Here is a brief
review of the rules of significant figures.
First, let us define significant digits.
Nonzero digits are always significant.
Zeros are significant if
they occur between nonzero digits (e.g. 504) or if they occur to the right of the decimal point as trailing
zeros (e.g.
4.50
!
10
3
). Leading zeroes as in 0.00045 are not significant, as they function only as
placeholders for the two significant digits.
Here are two simple rules for rounding the reported uncertainty:
1.
Round your error to one (the first) significant figure unless the first digit is ‘1’.
If it is ‘1’, keep
the next digit too.
Taylor also argues that this can be done if the first digit is ‘2’.
2.
Round your value so that its last significant digit is in the same position (or place value) as the
last significant digit of the uncertainty.
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2
Question 0.1
You are measuring the mass of a paperclip on a digital scale.
The measured value fluctuates between
1.01 and 0.90 grams.
What value will you record for the mass and its uncertainty?
1.2
Estimating Uncertainty
Each time you wish to determine the value of a measurable quantity there will be an associated
uncertainty in that measurement.
Even the most precise instrument has limitations.
If your measured
quantity is consistent over time and the smallest increment of measured precision is greater than random
fluctuation, then your rough estimate of error will be the smallest single increment of the used scale.
For
example, if you measure length with a ruler with hashmarks every 1/16 of an inch, then you would
decide which hashmark is closest for your measurement and your uncertainty would be 1/16 of an inch.
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 Spring '08
 Bodde
 Oscilloscope, Electronic test equipment, Significance arithmetic

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