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MMO 193 Moscow MO 1951 first 3 figures after the decimal point

Source:

August 7, 2019
decimal representationalgebra

Problem Statement

Prove that the first 3 digits after the decimal point in the decimal expression of the number 0.123456789101112...4950510.515049...121110987654321\frac{0.123456789101112 . . . 495051}{0.515049 . . . 121110987654321} are 239239.
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