Question

if p,q are co primes and q=2^n.5^m, where m>n then find after how many places the decimal of p/q terminates?

Answer 1

Given : p,q are co primes and q=2^n.5^m, where m>n

To find : after how many places the decimal of p/q terminates

Solution:

p,q are co primes

q = $2^n.5^m$

m > n

hence after m decimal places the decimal of p/q terminates

p/q  = p /$2^n.5^m$

multiplying numerator & denominator by $2^{(m-n)}$

=> p/q  = p . $2^{(m-n)}$ /$2^n.5^m$.$2^{(m-n)}$

=> p/q  = p . $2^{(m-n)}$ /$2^m.5^m$

=> p/q  = p . $2^{(m-n)}$ /$10^m$

Hence decimal of p/q  terminates after m places

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