according to physics  number of significant digits do matter as it leads to aacurate measurement, so for eg 420 so here there would be 2sf but in mathematics if we see 420 or 420.0 so we consider both as a same value but in physics there are looking different due to significant figures so  do we have to follow physics rule or mathematics rule in the numerical question?

The zeros are place holders UNLESS it is specifically stated that the zeros are significant.
Example  420
Explanation Only the first two digits are significant . The extra zeroes are acting as place holders, and unless we are told otherwise, we assume that the zeroes are not significant.
So while doing calculations we will consider 420 but writing 420.0 is more precise if the problem which you are dealing with deals with 4 significant numbers.

Significant digits are a way to give solutions in a way that is as accurate as the question. They present a set of rules for rounding off answers to an appropriate number of decimal places. In general, the number of decimal places we end up using is dictated by how accurate our measurements are. This insures that the final answer is just as accurate as the measurements that went into determining it.

So while rounding off significant numbers matter

420 contains 2 significant figures. 420 rounded and to 1 sig figs is 400. To count the number of sig figs in 420, strip the trailing insignificant digits (0) to get the significant digits (42).


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