Solve Uncertainty with Significant Figures: a-d

[Noor123]

Uncertainty?? URGENT HELP

How do you answer this? I totally don't get it. What do I do to calculate the uncertainty percentage??

Q. The number of significant figures reported for a measured value suggests a certain degree of precision.
What is the relative uncertainty implied by the following numbers?
a) 0.30 implies an uncertainty of ± _____ %
b) 9.8 implies an uncertainty of ± _____ %
c) 52 implies an uncertainty of ± _____ %
d) 0.503 implies an uncertainty of ± _____ %


Answers:
a) 0.30 implies an uncertainty of ± 3 % (possibly 2% from rounding error)
b) 9.8 implies an uncertainty of ± 1 % (possibly 0.5% from rounding error)
c) 52 implies an uncertainty of ± 2 % (possibly 1% from rounding error)
d) 0.503 implies an uncertainty of ± 0.2 % (possibly 0.1% from rounding error)

 

[Noor123]

BUMP!

does anyone know?

 

[renacat]

Think about what numbers could be rounded up or down to get these numbers, for example the biggest number that rounds down to 0.30 must be less than 0.305. The smallest number that can be rounded up to 0.30 is 0.295. So 0.30 is plus or minus 0.005.

0.005 is 1.67% of 0.30.

 

[Noor123]

but how do you know that it's 0.005? or why do you choose it?

 

[Lemm]

yes uncertainty in this case is half of the smallest unit +/-, but i think that in this case they are asking the uncertainty percent
After getting your uncertainty for example 9.8 is +/-0.05 units, this means that this might have rounded your value a maximum of .1 up or down so you simply get that .1 and divide by 9.8 which gives the corresponding 1%
(Im not completely sure about this, but it seems to work for all the anwsers and makes sence)

 

[Lemm]

For example if your measuring something your uncertainty is half of the smallest measuring unit on your instrument +/- because you can't be certain of your measurement if its between two scale marks and you could round it up when indeed its down, or viceversa

 

[Noor123]

Got it!

Thank a lot folks!