This question already has an answer here:
Please look at this computations:
a = N[Sqrt, 20]; N[a^2, 100]
The output is 2.0000000000000000000, which is apparently not $a^2$ to 100 decimal places.
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You can see how accurate a number is represented using the
Hence, when printing out N[a^2,100], only the first 20 (or so) digits are significant and are printed. This is also true in general, for example:
The product is returned only with the accuracy of the least accurate of its two components. If you want greater accuracy, you can specify more digits (as you suggest in your comment) or you can keep things infinitely accurate by using rationals. Compare:
The first two are both approximate (and calculated to the accuracy of the inputs), while the third is exact. If you want to work with reals, then you can set the accuracy to a specified number. For example, with
So I guess the short answer is that