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Examine whether the following numbers are rational or irrational:$ 1.101001000100001 \ldots . . $
Given:
\( 1.101001000100001 \ldots . . \)
To do:
We have to classify the given number as rational or irrational.
Solution:
A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.
The decimal expansion of \( 1.101001000100001 \ldots . . \) is non-terminating and non-recurring.
Therefore, \( 1.101001000100001 \ldots . . \) is an irrational number.
Updated on: 10-Oct-2022
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