Product of digits

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

AA is the sum of F(x)F(x) over all 2-digit numbers (i.e. 10x9910 \leq x \leq 99)

BB is the sum of F(x)F(x) over all 3-digit numbers (i.e. 101x999101 \leq x \leq 999).

Find BA\frac{B}{A}

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