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

Evaluate the meaning: Evaluate the meaning of -0. bar(32). -0. bar(32) means -0.323232..., which is a repeating decimal.Convert to a fraction: Convert the repeating decimal to a fraction. Let x = -0. bar(32). Then, 100x = -32. bar(32). Subtracting the original equation from this new equation gives: 100x - x = -32. bar(32) - (-0. bar(32)) 99x = -32 x = -32/99Identify rational or irrational: Identify whether the fraction is a rational or irrational number. The number -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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Is the following number rational or irrational?

-0. bar(32)
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational? $\newline$ $-0.\overline{32}$ $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational

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Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. Is the following number rational or irrational?

\newline

-0.\overline{32}

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

Evaluate the meaning: Evaluate the meaning of $-0.\overline{32}$ . $\newline$ $-0.\overline{32}$ means $-0.323232\ldots$ , which is a repeating decimal.
Convert to a fraction: Convert the repeating decimal to a fraction. $\newline$ Let $x = -0.\overline{32}$ . Then, $100x = -32.\overline{32}$ . $\newline$ Subtracting the original equation from this new equation gives: $\newline$ $100x - x = -32.\overline{32} - (-0.\overline{32})$ $\newline$ $99x = -32$ $\newline$ $x = -\frac{32}{99}$
Identify rational or irrational: Identify whether the fraction is a rational or irrational number. $\newline$ The number $-\frac{32}{99}$ is a fraction, which means it is a rational number because it can be expressed as the quotient of two integers.