Calculate $\frac{\pi}{\sqrt{2}}$ to three decimal places.
Let's assume that $\pi$ and $\sqrt{2} n$ are given with $n$ decimal places, and furthermore, $\pi$ is in a lower and $\sqrt{2}$ in an upper approximate value. Since the integer part in both is single-digit, the absolute errors $e$ and $e_{1}$ are smaller than one unit of the $n+1$-th digit, so the relative errors $e^{\prime}$ and $e_{1}^{\prime}$ are smaller than $\frac{1}{10^{n}}$.

But the relative error of the quotient

$$
E^{\prime}<e^{\prime}+e_{1}^{\prime}<\frac{2}{10^{n}}<\frac{1}{10^{n-1}},
$$

so the absolute error of the quotient is smaller than one unit of the $n-1$-th digit. Since the integer part of the quotient is a single digit, the $n-1-1$-th digit is the $n-2$-th decimal, so

$$
E<\frac{1}{10^{n-2}}
$$

Thus, the quotient is accurate to $n-2$ decimals if $\pi$ and $\sqrt{2} n$ are taken with $n$ decimal places. If we want the quotient to contain 3 accurate decimals, $\pi$ and $\sqrt{2}$ must be taken with $5-5$ decimal places. These values are $\pi=3.14159$ and $\sqrt{2}=1.41422$, whose quotient is 2.221 as a lower approximate value.

(Visnya Aladár, fóreálisk. VIII. o. t. Pécs.)

The problem was also solved by: Friedmann Bernát, S.-A.-Ujhely; Grünhut Béla and Kohn Márkus, Pécs; Galter János, Sz.-Udvarhely.