A student considers the decimal number obtained by writing the natural numbers one…
MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems
Problem
A student considers the decimal number
0.1234567891011121314…
obtained by writing the natural numbers one after another after the decimal point.
(a) Examine the sequence of digits and explain whether any fixed block of digits repeats after a finite stage.
(b) On the basis of your observation in part (1), state with reason whether this number is rational or irrational.
(c) Write a brief summary of the rule that links the type of decimal expansion of a real number with its classification as rational or irrational.