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e-zero
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I have a question which states that a car's speed is 110km/h. Should I assume this speed to be 3 significant figures or 4 significant figures? why??
Borek said:I was always under impression that in most physics courses nobody cares about sig figs, they are treated seriously only by chemists (and even then not by all).
technician said:They are treated as a means of assessing and conveying accuracy but it would be laborious if every example had to have this error analysis applied.
e-zero said:Would you equate that to 3 significant digits or 1? I am suggesting 1 because the numerator & denominator of the fraction 1/2 are both composed of 1 significant digit.
e-zero said:How about this example: 130km / 95km/h
Would your answer be 1.37h or 1.4h?
AlephZero said:If you want to estimate the error in the answer, then do it properly.
"Counting significant figures" is such a crude method as to be no real practical use. If the answer happens to be 99, then to 2 significant figures you have an error of about 1%. If it happens to be 101, to 2 s.f. you have an error of about 10%. If you think that makes any sense, then carry on counting significant figures...
Edit: I started typing this before jtbell's post appeared.
e-zero said:I'm still a little confused. How about 65 * 1.96
What would you state that answer as?
technician said:
101 is not given to 2 significant figures, it is 3. 101 means you know it is not 100 and it is not 102.
about 1% variation.
The problem arises when a value of 100 is quoted I would say
technician said:65 x 1.96 this could represent the length of a steel bar and the width of the steel bar. If you are required to calculate the area then only 2 figures should be used because the 65 could be a value anywhere between 64 and 66 whereas the 1.96 could be any value between 1.95 and 1.97.
technician said:The whole idea of significant figures is to do with reporting measurements which must have some degree of uncertainty about them.
technician said:Do you have any advice about sig figs that is constructive?
Do you know how the use of sig figs is taught in schools?
e-zero said:Let me use an example to see opinion: ½(23.1 cm3 − 20.32 cm3 + 19.0 cm3)
Would you equate that to 3 significant digits or 1? I am suggesting 1 because the numerator & denominator of the fraction 1/2 are both composed of 1 significant digit.
tiny-tim said:that's addition (and subtraction), so you don't use significant figures anyway, you use decimal places …
you use the highest decimal place of the given numbers, in this case one decimal place after the decimal point
then you divide by 2 which is exact (ie a million billion trillion sig figs)
e-zero said:½(23.1 cm3 − 20.32 cm3 + 19.0 cm3) * 6cm3
then you would have to round to 1 significant figure.
correct?