Question

a rational number in its decimal expansion is 327.7081 . what can you say about the prime factors of q, when number is expressed in the form of p/q ? give reason

Answer 1

Well, since the decimal expansion is terminating, we can say that q was a number which was a number of the form 2ᵃ5ᵇ. Since the number of digits after decimal terminate after 4 digits, we can correctly assume q to be 10000 or 2⁴5⁴. 

Answer 2

Answer:

the prime factor of q is 2 and 5

Step-by-step explanation:

327.7081 =  $\frac{3277081}{10000}$ = $\frac{p}{q}$

= $\frac{3277081}{(10)^{4} }$

=$\frac{3277081}{(5*2)^{4} }$

=$\frac{3277081}{5^{4} * 2^{4} }$

The denominator is in the form of $2^{m}* 5^{n}$

∴The prime factor of q is 2 and 5