if in the case of 3.16 if we truncate to tenths place we can chop of the digits beyond tenths place but why in the case of 32 we can't literally "remove" digits, but change them to zero.Why not chopping off
Do you not understand that truncation is a form of rounding, which yields a number close to the number you start with? Changing 32 to 3 is nothing like rounding. Suppose that truncation to the tens place is not defined anywhere, and we want to define it for that case; wouldn't we want to define it in a way that makes sense, rather than one that is useless?
The
Wikipedia article on truncation doesn't restrict it to truncation to an integer, but only talks about leaving n digits to the right of the decimal point, so we can't really apply their definition to your question; but in fact the formula they give, for positive numbers, does work:
[MATH]trunc(x, n) = \dfrac{\lfloor 10^nx\rfloor}{10^n}[/MATH], so [MATH]trunc(32, -1) = \dfrac{\lfloor 10^{-1}\cdot 32\rfloor}{10^{-1}} = \dfrac{\lfloor 3.2\rfloor}{0.1} = \dfrac{3}{0.1} = 30[/MATH]
We could probably find a source that talks about this case (probably calling it "rounding down", as truncation is usually, if not always, used of decimals); but why are you pursuing this case, which seems to be irrelevant to your original question?