354

Part of 1983 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

k

n

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)

times. Prove that the obtained number

m

satisfies inequality

m < \frac{18k}{13}

. (Examples of rounding:

191\to190\to 200, 135\to140\to 100

inequalitiesalgebraDigits