Question 35
For $x$ a positive real number with finitely many decimal places, denote by $r(x)$ the number formed by reversing the digits and decimal point of $x$. For instance, $r(98.6)=6.89$ and $r(740)=0.047$.
a. Prove that for all positive real numbers $x$ and $y$ with finitely many decimal places,
$$
r(x y) \leq 10 r(x) r(y) .
$$
b. Determine whether there exist values of $x$ and $y$, each having at least 2015 nonzero digits, such that equality holds.
a. Prove that for all positive real numbers $x$ and $y$ with finitely many decimal places,
$$
r(x y) \leq 10 r(x) r(y) .
$$
b. Determine whether there exist values of $x$ and $y$, each having at least 2015 nonzero digits, such that equality holds.