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Re: Significant figures - a Modest Proposal



On Mon, 30 Aug 1999, Leigh Palmer wrote:

At 06:03 -0700 8/30/99, Robert A Cohen wrote:

While I'm on the topic, I should mention that I will be emphasizing the
distinction between precision and resolution and that both contribute to
the accuracy of the measurement (I haven't done so in the past). The
activity above is designed to introduce the idea of resolution and its
effect on calculations. The second activity is designed to introduce the
idea of precision and its effect on calculations (they time cars and see
how many are speeding - the timer provides measurements to the hundreths
of a second but the precision is not that good). If anyone has any
experience with teaching this, I'd appreciate pointers.

Please amplify this somewhat. I think I have always treated resolution
and precision as being nearly identical in meaning. What are your views
on that topic, which I do consider to be very important?

When the students use a hand-held timer to time an object, the timer
provides a reading down to the hundreths of a second. The resolution of
the measurement is about 0.01 s.

However, the measurement is not accurate to 0.01 s. Due to reaction time,
the measurement cannot be repeated exactly the same from case to case.
For example, when timing a ball that is dropped from about a meter, most
students obtain a spread in their timings of about 0.1 s.

In other words, the precision is on the order of 0.1 s and the resolution
is on the order of 0.01 s.

There may be other contributions to poor accuracy, e.g., bias in reaction
time, parallax, poorly calibrated timer, etc.; here I am only discussing
the distinction between resolution and precision. BTW, because precision
refers to the repeatability of a measurement, poor precision can be
addressed somewhat by multiple readings, whereas poor resolution cannot.

I'm not an expert on error analysis so I may be mistaken about this. If
so, I'd appreciate if someone would set me straight before I mislead all
of my students.

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| Robert Cohen Department of Physics |
| East Stroudsburg University |
| bbq@esu.edu East Stroudsburg, PA 18301 |
| http://www.esu.edu/~bbq/ (570) 422-3428 |
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