If you had to approximate the value of $\frac{10^6 - 11}{2^{12}}$ quickly and in your head, how would you do it? (The real value is 244.14)
The way I done it on paper was $\frac{10^6 - 11}{2^{12}} \approx \frac{10^6}{2^{12}} = (\frac{5}{2})^6 = (2+ \frac{1}{2})^6$, and then expanded, ignored the $\binom{6}{6}\frac{1}{2^6}$ and approximated $\frac{6}{16}$ to 0.38, from which I ended up with the value 244.13. However this doesn't seem completely viable if had to be done without writing anything down, especially in a time pressured scenario. So I wonder how to go about finding an approximation method that can be done in my head, but also gives a decent approximation to the true value.