finding nearest perfect square for a fractional number Is it possible to have a clear definition for the nearest perfect square number for a fractional number? For example, let us consider a number 0.004. What is another decimal number closest to it, that is also a perfect square? Is it 0.0025? We know 0.0025 is a perfect square (0.05*0.05) but is it the closest one? Is there any way to find out?
(PS : please suggest some tags for questions like these)

Note that $$0.004=\frac{4}{1000}.$$
Now, let's "zoom in" one digit.  Change the denominator to $10000$, and bring the numerator to the nearest perfect square integer to $40$ - that'd be $36$.
$$0.0036=\frac{36}{10000}=\left(\frac{6}{100}\right)^2.$$
This is closer to $0.004$ than $0.0025$, for sure.  But is it the closest?  Let's try it again.  What if we look for stuff of the form $(x/1000)^2$?  We need the closest perfect square to $4000$ - that's $63^2=3969$.  Now we have $$0.003969=\frac{3969}{10000}=\left(\frac{63}{1000}\right)^2.$$  That's even closer.  Let's go one deeper... $$0.00399424=\frac{399424}{100000000}=\left(\frac{632}{10000}\right)^2.$$
Can you see what's happening here?
