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I state a problem from my book : Find the number of significant figures in $V_A=11.2461$ given its absolute error as $0.25×10^{-2}$.

Now I thought that significant figures refer to those digits that give meaning to the representation of a number and are not there just as placeholders. I would say that the number of significant figures in the number provided is 6. However, their approach was : Absolute error is less than half a unit in hundredths place. So it is correct to two decimal places. Hence the number of significant figures is 2+2=4.

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Normally the digits given are an indication of the possible error in the number and you can just count them as you have done. If you just see the value $11.2461$ you assume the error is something like $\pm 0.00005$. Here you are told what the possible error is, which is $\pm 0.0025$. The range of the true value is $11.2436$ to $11.2486$. You can see that only the first two decimals are known.

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  • $\begingroup$ I Understood that. But this goes against the definition of significant figures that I've known for all this time. $\endgroup$ – Hrit Roy Nov 4 '17 at 14:14
  • $\begingroup$ Oh also, according to our definition, the range isn't 11.2436 to 11.2486, but those two numbers are in fact the two possible true values of the number. $\endgroup$ – Hrit Roy Nov 4 '17 at 14:18
  • $\begingroup$ I'll just assume they meant how many significant figures is $V_A$ correct to $\endgroup$ – Hrit Roy Nov 4 '17 at 14:30

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