Question

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

Answer 1

Answer:

We know that the terminating decimal must be the one which has a finite decimal digits which ends exactly at a point and we cant find any repetitions of the decimal values thereafter. The terminating decimal can be represented in the form of a fraction since the value of the fraction terminates at some point.

Since the rational number 327.7081 is a terminating decimal, it has to be in the form of a/b where, b, the denominator, must be of the structure $2^x \times 5^y$ .

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