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Answer:
.
Step-by-step explanation:
A number is a rational number if and only if it is equal to the ratio between two integers. In other words, a number is a rational number if and only if there are integers (whole numbers)
and
(
) such that
.
Thus, the in this question would be a rational number as long as there are integers
and
(
) such that
. Simply finding the right
and
would be sufficient for showing that
is rational.
Since is a terminating decimal, one possible way to find
and
is to repeatedly multiply
by
until a whole number is reached:
.
.
.
Thus, , such that
and
(both are integers, and
) would ensure that
.
Therefore, is indeed a rational number.