Question about Measurements and sig. figs.

In summary: So basically, the last digit of a measuring device's display is the digit that counts down from 10. This is different from the precision of the instrument, which is given in the instrument's specifications. For example, an analog ammeter may have a precision of +/-0.1mm.
  • #1
junior_J
46
0
This is a question about practical physics ... if its posted in the wrong section my sincere apologies !

How do i decide the least count of a measuring device such as an ammeter (analog) ?
I know that the least count is the smallest division of measurement ... but why do people take the measurement to the nearest half division ?
Does it have something to do with the pointer(needle) of the ammeter ?? may be its thickness ... i have the same problem with understanding why a measurement made by a metre rule with a least count of 1mm is quoted as say (1.25+/-0.05)cm .
 
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  • #2
A good instrument normally has a specification of the precision of the reading, but it for sure isn't better than the last digit (otherwise the manufacturer would have added digits !). Also, most serious manufacturers don't make a fool of themselves by providing totally meaningless digits.

So if you have no specific indication, then guessing that one unit of the last digit is in the ballpark of the error on the measurement is often, with lack of better knowledge, a good idea. But for any serious error study, you should look at the detailled specifications of precision of the instrument, as given by the manufacturer.

You consider that the display of an analog instrument is digitized by the finest grading scale you are using.
If the error is 1 scale jump, then you can model that by +/- 0.5 a scale jump. Remember, in any case you're guessing here, and an order of magnitude for the error is the best you can get this way. If you want to have a better estimate of your error, you should consult the documentation of the instrument.
 
  • #3
So if you have no specific indication, then guessing that one unit of the last digit is in the ballpark of the error on the measurement is often, with lack of better knowledge, a good idea.

Im sorry i don't understand ... ! Can u elaborate a bit more . what last digit ??

Ive skimmed through some textbooks and websites ... What i don't understand is why some quote the uncertainty for a regular metre rule as
+/-0.05mm and others as +/-0.1mm ... and what's the difference between the two ? The same thing with the analog ammeters ...

Thank u !
 

1. What are significant figures and why are they important?

Significant figures are the digits in a number that represent the precision of a measurement. They are important because they indicate the level of accuracy and precision in a measurement. They also help to avoid rounding errors and ensure consistency in calculations.

2. How do I determine the number of significant figures in a measurement?

The general rule is to count all non-zero digits and any zeros between them. For example, the number 123.45 has five significant figures. Zeros that are placeholders or at the end of a number may not be significant, such as 0.003, which only has one significant figure.

3. Can I round off significant figures when performing calculations?

Yes, you can round off significant figures when performing calculations, but the final result should have the same number of significant figures as the measurement with the least number of significant figures. This helps to maintain the same level of precision throughout the calculation.

4. What is the significance of trailing zeros in a measurement?

Trailing zeros after a decimal point are always significant and should be included in the total number of significant figures. However, trailing zeros before a decimal point are not significant and are only used to indicate the magnitude of a number.

5. Can significant figures be used in non-numerical measurements?

Yes, significant figures can be used in non-numerical measurements, such as counting objects or recording time. In these cases, the significant figures represent the estimated or measured quantity, and the final result should have the same number of significant figures as the measurement with the least number of significant figures.

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