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ASU 354 All Soviet Union MO 1983 inequality in rounding in tens

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July 28, 2019
inequalitiesalgebraDigits

Problem Statement

Natural number kk has nn digits in its decimal notation. It was rounded up to tens, then the obtained number was rounded up to hundreds, and so on (n−1)(n-1) times. Prove that the obtained number mm satisfies inequality m<18k13m < \frac{18k}{13}. (Examples of rounding: 191→190→200,135→140→100191\to190\to 200, 135\to140\to 100.)
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