Question

I use a thermometer graduated in 1/5 degree Celsius to measure outside air temperature. Measured to the nearest 1/5 degree, yesterday's temperature was 22.4 degrees Celsius and today's is 24.8 degrees Celsius. What is the relative uncertainty in the temperature difference between yesterday and today?

Answer 1

the uncertainty in the difference is \( 2 \times (1/5)=0.4\) degrees, so the relative uncertainty, is:
\[\huge \frac{{0.4}}{{\left( {24.8 - 22.4} \right)}} \times 100 = ...\% \]

Answer 2

Thanks though mehn but that's not correct.

Answer 3

I tried that

Answer 4

the answer is actually 7.7%

Answer 5

the measured temperatures, are:
\[\Large \begin{gathered}
\left( {22.4 \pm 0.2} \right) \hfill \\
\hfill \\
\left( {24.8 \pm 0.2} \right) \hfill \\
\end{gathered} \]

Answer 6

yes....I don't know why the answer behind the book itself is different

Answer 7

Apart from me and my textbook, you are the second person solving this question this way so I guess I am just going to write the answer that way .Could you please help with another question?

Answer 8

so, the difference, is:
\[\Large \Delta T = \left( {2.4 \pm 0.4} \right)\]

Answer 9

yes

Answer 10

My digital watch gives a time reading as 09:46. What is the absolute uncertainty of the measurement?

Answer 11

I tried to use the theory of propagation of uncertainties, namely I write this:
\[\Large \delta = \sqrt {{{0.2}^2} + {{0.2}^2}} \simeq 0.283\]
as uncertainty on the temperature difference
nevertheless I haven't got the result above

Answer 12

is your watch able to read the \(1/100\) of second ?

Answer 13

the question doesn't state

Answer 14

what is the minimum quantity which can be measured by your watch, then?

Answer 15

the question doesn't state, but I just assumed it should be like 1 minute

Answer 16

therefore, we can write this:
\[\Large \left( {9.77 \pm 0.02} \right)\;hour\]

Answer 17

but the answer in the book is 0.5 minutes

Answer 18

This was what I did I said that the actual time should be between 9:45 to 9:46

Answer 19

ok! It is a possible choice
usually, when I was at laboratory course, I took the minimum measured quantity as uncertainty

Answer 20

so it's correct then? Is that what you are saying?

Answer 21

if the measure instrument is new, then we can take \(1/2\) of the minimum measured quantity as uncertainty, otherwise, it is better to take the same minimum measured quantity as uncertainty

Answer 22

ok thanks then...God bless you. Bye

Answer 23

:)