Question
Which one of the following is a correct statement?
✓
Answer
- Decimal expansion of an irrational number is non-terminating and non-repeating.
Solution:
Decimal Expansion of a Rational number is not only terminating,
It can be either terminating like $\frac{1}{2}=0.5$ or non-terminating Repeating like $\frac{1}{3}=0.3333333......$ So option (a) is not true alone.
Now we know that Non-Terminating numbers are of two types:
One is Non-Terminating Repeating and other is Non-Terminating Non-Repeating.
The Decimal expansion of a Rational number matches one of it's kind i.e Non-Terminating Repeating of Non-Terminating numbers.
So Rational number does not consist both the kinds of Non-Terminating numbers.
Hence, they are not Non-Terminating numbers.
An irrational number is always Non-Terminating in nature, but again not of both of it's kinds.
The decimal Expansion of an irrational number is Non-Terminating Non-Repeating in Nature.
So from all above points and theory we can conclude an Irrational number is Non-Terminating but Non-Repeating in nature
i.e. $\sqrt{2}=1.4142135623730...$
So, option (d) is correct.
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