By what factor is $8\times 10^{-3}$ larger than $2\times 10^{-6}$?

Divide: $\frac{8\times 10^{-3}}{2\times 10^{-6}}=\frac{8}{2}\times 10^{-3-(-6)}=4\times 10^3=4000$. Dividing only the decimal parts and ignoring the powers of ten gives the trap 4, and miscounting $-3-(-6)$ as 2 gives 400.