Question

A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q , when this number is expressed in the from p/q? Give reasons.

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Answer 1

Answer:

A rational number in its decimal expansion is 327.7081

it means that it is terminating

and for decimal expansion to be terminating prime factors of q must include 2^m and 5^n

Answer 2

Answer:

Step-by-step explanation:

The decimal expansion of a rational number is either terminating or non terminating repeating

In the above case of 327.7081 the decimal expansion is terminating. So in the p/q form it can be written as

3277081/10000

The prime factors if q (10000 in this case) is if the form 2^m × 5^n where m and n are positive integer

So we can say that if the prime factors of q contains either 2 or 5 ior both 2 and 5 then the decimal expansion is terminating.