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Is the following number rational or irrational? -0. bar(32) Choose 1 answer: (A) Rational (B) Irrational

Is the following number rational or irrational?\newline−0.32‾-0.\overline{32}\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational

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Full solution

Q. Is the following number rational or irrational?\newline−0.32‾-0.\overline{32}\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational
  1. Evaluate the meaning: Evaluate the meaning of −0.32‾-0.\overline{32}.\newline−0.32‾-0.\overline{32} means −0.323232…-0.323232\ldots, which is a repeating decimal.
  2. Convert to a fraction: Convert the repeating decimal to a fraction.\newlineLet x=−0.32‾x = -0.\overline{32}. Then, 100x=−32.32‾100x = -32.\overline{32}.\newlineSubtracting the original equation from this new equation gives:\newline100x−x=−32.32‾−(−0.32‾)100x - x = -32.\overline{32} - (-0.\overline{32})\newline99x=−3299x = -32\newlinex=−3299x = -\frac{32}{99}
  3. Identify rational or irrational: Identify whether the fraction is a rational or irrational number.\newlineThe number −3299-\frac{32}{99} is a fraction, which means it is a rational number because it can be expressed as the quotient of two integers.

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