Question

the+decimal+expansion+of+K/2^5*3^2+is+terminating.The+value+of+K+can+be+equal+to

Answer 1

Solution:

It is given that,

$\frac{K}{2^{5}\cdot3^{2}}$ is a terminating decimal.

We should make the Denominator of the form (2^n × 5^m)

K = 5^5 × 3²

Now ,

K/[2^5×3²]

= (5^5×3²)/[2^5×3²×5^5]

= 28125/(2^5×3²×5^5)

Therefore,

K = 28125

Verification:

K/[2^5×3²]

= 28125/[2^5×3²×5^5]

= 3125/[2^5×5^5]

= 3125/(2×5)^5

= 3125/10^5

= 0.03125 [ terminating decimal]

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