IIT JEE , AIEEE Forum - Mathematics , Algebra

pantpranav

In a fraction and its decimal notation every letter represents a digit. Different letters denote different digit. Numerator and denominator are mutually prime. Determine the value of the fraction.
ADA/CDC = .EFGHEFGHEFGHEFGH................
Where A,B,C,D,E,F,G,H denote the digits.

elastiboysai

Hi Pantpranav,

I'm not sure if its possible

here's why

ada/cdc =.efgh' (' notes repetit. here )

10000ada/cdc=efgh.efgh'

subtract n u get

9999ada/cdc=efgh

so ada/cdc=efgh/9999

now

we must have some common factor between

efgh and 9999 such dat dey cancel out to give

a fraction of the form ada/cdc

now dis is possible only if

d common factor is 11.(u can check upon dat oderwise u wuldn end up wid such a fraction)

but, wid 11 common

u d=0

but if d=0

ada and cdc will always have comm factor 101 and not be utually prime

Bt i'm not sure abt dis.

jus chec.

elastiboysai

Hi

Anoder simple observation:

plug in any no coprime wid 9999 in the calc. divide it by 9999

u get a no. of d form .efghefghefgh...

now plug in any no. wid a comm factor n u don get .efgh'

bt here 2 get a no.,of form ada/cdc

it shudn b coprime( 2 get a 3 dig no.)

so we cant get a dec of d reqd form.

This is nt a rigorous soln

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