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Is 23\frac{2}{3} an irrational number?\newlineChoices:\newline(A) yes\newline(B) no

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Identify rational and irrational numbersright chevron icon

Full solution

Q. Is 23\frac{2}{3} an irrational number?\newlineChoices:\newline(A) yes\newline(B) no
  1. Define 23\frac{2}{3}: Step 11: Define the number 23\frac{2}{3}. 23\frac{2}{3} is a fraction where the numerator is 22 and the denominator is 33.
  2. Determine decimal type: Step 22: Determine if 23\frac{2}{3} is a terminating or repeating decimal.\newlineWhen we divide 22 by 33, the decimal 0.666…0.666\ldots repeats indefinitely.
  3. Define irrational numbers: Step 33: Define irrational numbers. Irrational numbers are numbers that cannot be expressed as a simple fraction and their decimal expansions are non-terminating and non-repeating.
  4. Compare with definition: Step 44: Compare 23\frac{2}{3} with the definition of irrational numbers.\newlineSince 23\frac{2}{3} is a repeating decimal, it does not fit the definition of an irrational number, which must be non-repeating and non-terminating.

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