Exam-style question
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Classify each quantity as precisely as possible: 12, -5/2 and √2. For each one, state whether it is natural, rational, irrational and real.
Model answer
What a good answer should say
- 12 is natural, rational and real.
- -5/2 is rational and real, but it is not natural.
- √2 is irrational and real, but it is not rational or natural.
Explanation
Why this works
The classification demonstrates set inclusion and the distinction between rational and irrational real numbers. A natural number such as 12 is also rational and real.
A negative fraction such as -5/2 is rational and real but not natural. √2 is an irrational real number.
Common mistake
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