State whether the given statement is true or false.

The decimal expansion of a rational number is terminating or non-terminating recurring.

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True

False

answer is A.

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Detailed Solution

Here, we have to find whether the decimal expansion of a rational number is terminating or non-terminating recurring.
We know that a rational number is one that can be written as

p q

where

q ≠ 0,

such as

14,

35,

etc.
The decimal expansion of a number in the form

p q

always comes to an end or begins repeating the same finite series of digits after a certain number of digits.
Take the rational number

712

for example. When you divide 7 by 12, you get decimal expansion of 0.58333333. As a result, it has a repeating group that never terminates.
Also, consider the rational number

28

as well, which expands to a decimal as 0.25 and is referred to as terminating.
As a result, a rational number's decimal expansion is either terminating or non-terminating recurring.
Thus, the given statement is true.
Hence, option (1) is correct.

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