State whether the given statement is true or false.

$6.412341234 …$ is an irrational number.

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True

False

answer is B.

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Detailed Solution

The given number is

6.412341234 …

A number whether rational or irrational could be decided by whether they are terminating or non-terminating.
A number is terminating if the digits following the decimal point are eliminated, as in 0.25. Non-terminating repeating numbers are another type of rational number. In this kind, the digits following the decimal do not end but instead recur, as in 0.131313.
Irrational numbers, on the other hand, are non-terminating, non-repeating numbers, such as 1.41465289.
Here, in the given number

6.412341234 …

the numbers after the decimal 4123 is repeating themselves.
Therefore, the number is non-terminating and repeating, which means it is a rational number.
Therefore, the number 6.412341234… is a rational number.
Thus, the given statement is false.
Hence, option (2) is correct.

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