Question

If all measurements in an experiment are taken up to the same numbers of significant figures, then mention two possible reasons for the maximum error.

Answer 1

Hint
In this question, we are asked to find the possible reasons for the maximum error, if all measurements in an experiment are taken up to the same number of significant figures. The maximum error will be caused due to the errors in measuring a quantity not extreme accurately and the quantities that have high powers in the formula.

Complete step by step answer
There are many reasons which may cause the errors in the final result of an experiment.
The measurement which is least accurate – When we calculate the difference, the change in the value of the parameter, mostly denoted using a delta symbol $(\Delta )$ shows a maximum error, as every digit of the difference is very important.
The measurement of a quantity which has maximum power in the case of formulae – Many of the formulae that we use have some quantities which have higher power than the others. The higher the power, more will be the number of digits present in it. Similarly, the least the power, the less will be the number of digits present in it. Thus, while computing, a huge difference will be obtained, if all the measurements are taken up to the same number of significant figures.
Therefore, if all measurements in an experiment are taken up to the same number of significant figures, then, the two possible reasons for the maximum error is the measurement which is least accurate and the measurement of a quantity which has maximum power in the case of formulae.

Note
The significant digits of any number are the digits in that number that carry meaningful contribution to its measurement resolution. For any number, the most significant position is the one with the highest value of the exponent and the least significant is the one which has the least exponent value.