Question

Let D be a recurring decimal of the form D=0.a1a2a1a2a1...,where digit a1 and a2 lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer when multiplied by D?

Answer 1

Answer:

its straight question

its straight questiongive D=0.abababab (say - 1)

its straight questiongive D=0.abababab (say - 1)Multiply both sides by 100 i.e

its straight questiongive D=0.abababab (say - 1)Multiply both sides by 100 i.e100D = ab.abababab (say - 2)

its straight questiongive D=0.abababab (say - 1)Multiply both sides by 100 i.e100D = ab.abababab (say - 2)now subtract 1 from 2 . That gives

its straight questiongive D=0.abababab (say - 1)Multiply both sides by 100 i.e100D = ab.abababab (say - 2)now subtract 1 from 2 . That gives99D = ab => D = ab/99... hence it should be multiplied by 99k to get an integer ab.