State whether the following statement is true or false.
Look at several examples of rational numbers in the form $p q$ (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). If q has the form $2 a × 5 b$ , $p q$ is a terminating decimal.

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True

False

answer is A.

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Detailed Solution

A rational number is any number that can be represented in

p q

with q greater than 0. Real numbers cannot be represented in the form

p q

, where p and q are integers and q is not equal to 0 is an irrational number.
If the rational numbers have only powers of 2 or 5, or both, then q must meet the requirement that the rational numbers always have an ending decimal expansion.
We'll look at a few examples of rational integers whose decimal representations end in