Question

if x=0.56125 is written in p/q form, where p,q are coprimes and q is the form 2^n * 5^m, then find the value of n and m

Answer 1

answer is given in the figure
n=5
m=5

Answer 2

given x = p /q = 0.56125

p /q = 56125 /100000

as p and q both are co primes there only factor must be 1

so let's simplify above value till co prime appears in numerator and denominator

= 56125 / 100000
=11225 / 20000
=2245/ 4000
=449/800

now these two 449 and 800 are co primes

q =800
= 2×400
= 2×2×200
= 2×2×2×100
=2×2×2×2×50
= 2×2×2×2×2×5×5
= 2^5 × 5^2

therefore

n = 5 and m =2