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Tell whether the following statement is true or false:

The number $0.120120012000120000 …$ is an irrational number.

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True

False

answer is A.

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Detailed Solution

We need to check whether the number

0.120120012000120000 …

is an irrational number or not.
The numbers which cannot be expressed in the form of

p q

is termed as irrational numbers.
The decimal expansion of irrational numbers is non-terminating non-recurring (repeating).
The given number is

0.120120012000120000 …

.
As, the number has non-terminating non-repeating decimal expansion, therefore it is an irrational number.
Therefore,

0.120120012000120000 …

is an irrational number.
Given statement is true.
Hence, option 1 is correct.

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