Math CentralQuandaries & Queries


Question from Ann, a parent:

2.236...<br />
What is the most specific category of numbers does this fall into? Rational or Irrational? Does the .... mean that it repeats?

Hi Ann,

The question is ambiguous. It is not clear what is meant by 2.236… . The three trailing dots are at times used for various things and it is not clear what is meant here. If the intention is to mean that the 236 is repeated the standard way to do this is to place a line over the 236, to read $2.\overline{236}$. If so then this is a rational number. If the three trailing dots is meant to indicate that the digits continue without a repeating pattern then the number is irrational. If this is a textbook problem then a careful reading might clarify the question. My guess is that since there is no bar over the 236 that it is intended to indicate an irrational number. Again, without further explanation the question is ambiguous.


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