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MMO 326 Moscow MO 1956 deleting after 2nd digit after decimal

Source:

August 19, 2019
number theoryalgebra

Problem Statement

a) In the decimal expression of a positive number, aa, all decimals beginning with the third after the decimal point, are deleted (i.e., we take an approximation of aa with accuracy to 0.010.01 with deficiency). The number obtained is divided by aa and the quotient is similarly approximated with the same accuracy by a number bb. What numbers bb can be thus obtained? Write all their possible values.
b) same as (a) but with accuracy to 0.0010.001
c) same as (a) but with accuracy to 0.00010.0001