Whether the following statement is true or false:

$3. 142857 ¯$ is an irrational number.

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True

False

answer is B.

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Detailed Solution

We are given a number as

3. 142857 ¯

.
We can observe that the all the digits after the decimal point are under the overline i.e.,

¯

, which means that they are repeating itself.
All rational numbers hold the property that their decimal expansions are either terminating or repeating.
Therefore,

3. 142857 ¯

is a repeating decimal and hence, a rational number.
This contradicts the given statement.
Hence, the given statement is false.
So, the correct option is 2.

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