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If a reading of a length on meter rod is 44.6cm with least count of 1mm And last point of the length is exactly on 44.6 not in between of 44.6 or 44.7 Then how is it doubtful?

Qmechanic
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Remy
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2 Answers2

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If you're confident that your measurement is exactly 44.6 cm, you would express this confidence by writing 44.60 cm. (Many computer systems will "helpfully" truncate the trailing zero, so sometimes this requires some care.) In that case the uncertain final digit is the zero. For example, on many rulers, the millimeter marks are 0.1 mm or 0.2 mm wide, so "exactly on the mark" requires some estimating of its own.

rob
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The answer may lie in the claim: "exactly on".

If you look under a microscope, then you are most likely not exactly on 44.6 cm. You may be at 44.6003 cm. That 0.0003 cm error was undetectable with your mm-scale ruler.

So, what if the error was not only 0.0003 cm, but 0.003 cm? Or maybe even 0.03 cm? Would you be able to detect that with your ruler?

  • If you answer yes, then write that to the number: 44.603 cm or 44.63 cm.
  • If you answer no, then stop writing.

The last detectable deflection is the error - the uncertainty - of your measurement equipment and thus of your measurement. And because you write all digits you are certain of, the last digit will always be where you are uncertain.

If you with your measurement of 44.6 cm are certain about the next digit as well, then write it. If it is a 0, then write that: 44.60 cm. This is then the minimum length that the ruler-plus-your-eyes can detect.

Steeven
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  • so in example the all three measurements 44.603,44.63and44.60 have last digit as doubtful whether it is 3 or 0 – Remy Apr 09 '18 at 14:51
  • @Remy Yes. The last digit is placed where the uncertainty "starts". 44.63 could just as well be 44.64 e.g. because we don't know the next digit (it could be a 7 for instance. We don't know). – Steeven Apr 09 '18 at 19:54
  • can it be zer0(0) as well the doubtful digit ? – Remy Apr 10 '18 at 06:02
  • @Remy Yes, that is what I noted in the last paragraph in the answer and also what rob wrote in his answer. 44.60 cm is a valid way to write a number that tells you that you are sure down to the second decimal digit. The fact that that second decimal digit is zero doesn't matter. – Steeven Apr 10 '18 at 06:15