The number $\frac{2}{5}$ cannot be represented exactly in IEEE $754$ double preciision. What is the closest machine number to $\frac{2}{5}?$ What is the relative roundoff error involved in storing this number?

Hint: Recall that in IEEE double precision, floating point mumbers are uniformly spaced in intervals $2^n,2^{n+1}$ with gaps $2^{n-52}.$ In other words, number between $2^n$ and $2^{n+1}$ may be represented as $x=2^n(1+k)$ where $k=1,2,3,$cdots,$2^{52}-1$ and $=2^{-52}.$