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Is 103\frac{10}{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 103\frac{10}{3} an irrational number?\newlineChoices:\newline(A) yes\newline(B) no
  1. Understand 103\frac{10}{3}: Step 11: Understand the nature of 103\frac{10}{3}.\newline1010 divided by 33 equals approximately 3.333...3.333..., which is a non-terminating, repeating decimal.
  2. Define irrational numbers: Step 22: Define irrational numbers. Irrational numbers are numbers that cannot be expressed as a simple fraction and do not have a repeating or terminating decimal pattern.
  3. Compare to definition: Step 33: Compare 103\frac{10}{3} to the definition of irrational numbers.\newlineSince 103\frac{10}{3} is a repeating decimal (3.333…3.333\ldots), it can be expressed as a fraction (103\frac{10}{3} itself).
  4. Conclusion: Step 44: Conclusion based on comparison.\newlineBecause 103\frac{10}{3} can be expressed as a fraction and has a repeating decimal, it is not an irrational number.

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