Zero Error of Screw Gauge Consider a screw gauge of 50 divisions on the circular scale. Till now I have used the following method to account for zero error in it.
If $x^{th}$ division on the circular scale coincides with the zero on the main scale , then zero error,$Z$ is given by:
$$Z=\begin{cases}
x,  & \text{if $x$ < 25} \\[2ex]
x - 50, & \text{if $x$ > 25}
\end{cases}$$

What would be the zero error if $x= 25$, i.e., if 25 divisions coincide with the zero of the main scale?
Will it be a positive error or a negative error?

Please note that I am relatively new to experimental Physics.
 A: The thing referred to as "zero error" in the question is an offset which can in principle be corrected for. Therefore it does not contribute to the imprecision of the final measurement, as long as it is corrected for. For this reason one should be cautious about using the word "error" here. Having said that, the zero offset will itself only be known to some finite precision. Let's call this uncertainty $\Delta x_0$. The uncertainty of some other reading is $\Delta x$. The precision of the difference between these two readings is
$$
\sqrt{ \Delta x_0^2 + \Delta_x^2 }.
$$
So that is the quantity normally called the 'error' if one is using the instrument in a sensible way (i.e. taking the difference between the reading for the thing being measured and the reading for zero).
Actually a slightly more precise way to get the offset of a micrometer is to use it to measure something of non-zero size whose shape is similar to the thing you want to measure, and whose size is precisely known. This tends to avoid differences introduced by the way the jaws of the gauge close on each other compared to closing on something else.
How does all this answer the question? It answers it by saying that if you understand how you are going to allow for the zero offset then you understand whether it is positive or negative. And furthermore this is the only way to answer questions like this where a sign is concerned.
A: Zero error is basically a general term whose ERROR word is needed to be focused upon.The word error is something that we want to reduce so we use zero errors say x to say that this x quantity is to be subtracted. In screw gauge we use daily and basic principle of screw.The instrument has a screw touching a plate(I am not using technical terms).For measuring something we rotate the screw in a way to create space just enough to fit the body to be measured.this is basically rotating a screw to take out from wood.So now see we have zero at exactly the point with nothing.When we rotate the zero rotates and it gives us a number about how much we moved.In errors what happens basically is that the zero doesnt seem to signify nothing because it is already showing us some number as if something is being measured despite the screw touching the plate.So when we rotate it towards us to create space the numbers are added to something.We call a line at which the pointer points as reference line.This is where we look for the number we got for a measurement.
In errors we see that zero could be above reference line or below.For measurements we have to rotate it towards us only.If zero is above reference line it simply means that we have tightened the screw more than required.so zero went a bit up.It will show us some number on pointer.Since the numbers are marked from zero and above it in increasing sequence and if zero is above
Then obviously the 1 and 2 and so on will be above and what we will see is a big number on the pointer.Now when we will rotate it towards us few numbers will cross the pointer before zero will do so.What we could see in there will be a final number but we are aware that zero didnt cross it as soon as we started to rotate the screw.
For example as in ur case with 50 divisions lets say we had zero 3 divisions above the line i.e we are seeing 47 on pointer.We need to measure 5 division long rod and we rotate the screw but we can see that we took some extra divisions and after that zero crossed and gave us some measurement.But this measurement we got must be after zero crossed and we will have no info about the numbers it took before and it will give us a number of 2 on pointer.so we need to add some thing that is we have a negative zero error of 3. I hope you got it...i think now u should try to get that 25 dilemma on ur own for better and concrete memory.Refer to some pictures or better a real screw gauge if needed..
A: The method that you have used to account for zero error in screw gauge makes no sense for screw gauge zero error.


When the reading on the circular scale across the linear scale is more than zero (or positive), the instrument has a positive zero error as shown in case 1. When the reading of the circular scale across the linear scale is less than zero (or negative), the instrument is said to have a negative zero error, as shown in case 2.

As far as your question is concerned that what would be the zero error if 25 divisions coincide with the zero of the main scale? Will it be a positive error or a negative error? It is positive zero error in this case.
Reference
amrita.olabs.edu.in,. (2014). Screw Gauge. Retrieved 8 November 2021, from amrita.olabs.edu.in/?sub=1&brch=5&sim=156&cnt=1
