Let E=2.4583583583 be the number whose three–digit block 583 repeats without end.

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

Let

E=2.4583583583\ldots

be the number whose three–digit block 583 repeats without end. (a) Express

E

as an exact improper fraction in simplest form. Clearly indicate all algebraic steps. (b) Rewrite your answer from part (a) as a mixed number

A+\dfrac{B}{C}

with

B

and

C

relatively prime.