Discussion
If the decimal representation of a number is non-terminating, non-repeating then the number is
Answer: D
The decimal expansion sorts the real numbers into two kinds:
- Rational - the expansion either stops or falls into a repeating block, as in \( \tfrac{1}{4} = 0.25 \) or \( \tfrac{1}{3} = 0.333\ldots \)
- Irrational - it runs on for ever without ever repeating, as in \( \sqrt{2} = 1.41421356\ldots \) or \( \pi \)
A non-terminating, non-repeating expansion is therefore irrational. Natural and whole numbers are particular rationals with expansions that stop at once, so none of the other options can apply.
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