Product of digits

Let \(F(x)\) be a function which returns the products of the digits of \(x\). E.g. \(F(27)=14,F(248)=64\).

\(A\) is the sum of \(F(x)\) over all 2-digit numbers (i.e. \(10 \leq x \leq 99\))

\(B\) is the sum of \(F(x)\) over all 3-digit numbers (i.e. \(101 \leq x \leq 999\)).

Find \(\frac{B}{A}\)

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