The first thing that you have to know is that there is not exactly accurate measurement.
Error is anywhere. As a human, we cannot realize the hidden error that is caused by the environment and also the internal system of the measuring instrument.
Because we cannot spot the error, it’s reasonable we doubt the reading.
But, how doubtful we are to the reading? Is it very doubtful or not? Can we express the doubtful with numbers? Unfortunately, we have to express it.
Let’s say that a particular metallic object has a length of 1 inch. However, we are not sure that it’s exactly 1 inch because some hidden errors may happen. It may be because of the temperature or the measuring equipment we use has lost its accuracy (long time uncalibrated) or zero error may be happening.
We then estimate it must have extended for 0.002 inch. Oh no, it has shrunk for 0.002 inch because of the cold environment. At the same time, on the other hand, the zero error has occurred and affected the reading.
When we tell that the dispersion of measurement spreads among +0.002 inch and -0.002 inch (totally 0.004 inch), somehow we are still not sure it is. That might be due to we haven’t yet added another value. The zero error that may happen have to be considered.
However, when we tell the dispersion spreads among +0.003 inch and -0.003 (0.006 inch), our confidence to tell the true reading lies around it gets better.
We initially doubt the real reading, but the estimation has come and we are sure the exact measurement lies around those numbers.
The short descriptive text above explains how the uncertainty in measurement happens.
We need to remember that error in measurement is classified into two groups: systematic error and random error. The systematic error is the error that originates from the system, whether it’s mechanic or electronic system. This error can be spotted such as zero error. While the random error cannot be realized. It comes from the environment, the user, etc.
The random error is the main issue why uncertainty in measurement exists. It’s the thing where we register this uncertainty.
Scientists work hard to detail random error but it still exists. Therefore, it’s important to detail it with numbers and signs.
Uncertainty in measurement means the condition we are not confident to tell the true value lies at a certain point because there are some uncertainties from some undetected error sources. This is an advanced subject matter in measurement we have to learn.
No measurement is exact. Each measurement is an estimation only.
To express uncertainty, we use “±” and value (± 0.3 mm). It means we are sure that the answer is around those numbers (+0.3, +0.2, +0.1, 0.0, -0.1, -0.2, -0.3).
Uncertainty in measurement has a great correlation with accuracy. The smaller the range, the better it is.