Re: [Phys-l] [PTSOS] Significant Figures

[Bernard Cleyet <bernardcleyet@redshift.com>]

On 2011, Mar 19, , at 10:22, jonathanhanna wrote:

> Sure, I could just tell them to write down their measurements to the hundredths place each time, but I want there to be meaning behind why we write down "2.00" as oppose to "2" alone. Any suggestions?


If you forgot sig. figs. and taught estimated (or known probable error) you wouldn't have this prob.



Estimating error for single measurement is so easy, I can't understand why there is so much resistance to doing it.  e.g. using a meter stick w/ mm marks.  A valid estimation is +/- 0.5mm  A prob., especially in the 9th is derived values.  i.e. area -- but teaching as "received" knowledge,  RMS is a possible.  e.g.  L X W    each +/- 0.5 mm  multiplied the error is sqrt (0.5^2 + 0.5^2).

As soon as the students estimates the error, she knows how many figs. to write, both in the data and the final answer.  Obviously if the error is +/- 0.07 cm then 2. would be insufficient, and 2.0011 would be excessive for the final answer.   For data it's a good idea to have one or two extra "guard" figures if they are to be combined, e.g. volume from three measurements.  


Again read JD's page:

Measurements and Uncertainties versus Significant Digits or Significant Figures


In particular:


4.    If/when you wish to express the uncertainty, express it separately (rather than trying to use one numeral to represent two numbers). For example, an uncertain quantity can be properly expressed 1.234 ± 0.055, in which case we have one numeral (namely 1.234) to represent the nominal value, and a separate numeral (namely 0.055) to represent the absolute uncertainty. If you wish to express the relative uncertainty, as opposed to absolute uncertainty, it can be expressed using percentages, parts per thousand, parts per million, or something like that, e.g. 2900 ± 1.3% or equivalently 2900 ± 13000ppm.

bc wonders if there is a scientific journal that uses the number of figures to indicate error.

p.s.  Even the "the Physics Teacher" "shoulds" error limits as a separate number:

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Units and significant figures

Authors are encouraged to use SI units, but use of SI units is not mandatory in cases where other units are more appropriate. Measured and calculated numerical values should be written with the correct number of significant figures and include error limits.



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