I have read about significant figures in my chemistry and physics books, but none of them pointed out the significance of the significant figures.
Searching the Internet I found two possible answers: Some people are saying that it is to denote the accuracy and others are saying that it is to denote the precision of the measurement.
Both of these arguments are unsatisfactory, because in my opinion significant figures are not the only thing that governs the accuracy or precision of a measurement.
Layman's definition of accuracy and precision
Given a set of data points from repeated measurements of the same quantity, the set can be said to be accurate if their average is close to the true value of the quantity being measured, while the set can be said to be precise if the values are close to each other.
My arguments regarding significant figures, accuracy and precision:
Accuracy. Suppose I measure the weight of a candy using some device and get the measurement as 1.2 grams and then I measure it again using some other sophisticated device and got the answer 1.436575383 grams.
The first measurement is having two significant figures whereas the latter one is having 10 significant figures.
How can we say which measurement is accurate, if we don't know the actual mass of the candy? Here many might go for the latter measurement and will do all the calculations with that value. However, what if the second device was faulty, which was not known at the time of measurement.
Precision. Does a higher number of significant figures make a measurement more precise? How?
The larger the object I measure using the same device the higher is the number of significant figures displayed, but that does not make the measurements more precise.
Don't both, the precision and accuracy, depend on the operator of device?
So what is exactly the purpose of significant figures?