Is the following number rational or irrational? 6. bar(6) Choose 1 answer: (A) Rational (B) Irrational

Evaluate the meaning of 6. bar(6): Evaluate the meaning of 6. bar(6). 6. bar(6) means 6.6666..., where the digit 6 repeats infinitely.Convert the repeating decimal to a fraction: Convert the repeating decimal to a fraction. Let x = 6.6666... Then, 10x = 66.6666... Subtract the first equation from the second equation to get rid of the repeating part: 10x - x = 66.6666... - 6.6666... 9x = 60 x = 60 / 9 x = 20 / 3Determine if the fraction is rational: Determine if the fraction is rational. The number 20/3 is a fraction which represents a ratio of two integers (20 and 3), where the denominator is not zero. Therefore, 20/3 is a rational number.

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Is the following number rational or irrational?

6. bar(6)
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational? $\newline$ $6.\overline{6}$ $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational

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Math Problems

Algebra 2

Classify rational and irrational numbers

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Q. Is the following number rational or irrational?

\newline

6.\overline{6}

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

Evaluate the meaning of $6.\overline{6}$ : Evaluate the meaning of $6.\overline{6}$ . $\newline$ $6.\overline{6}$ means $6.6666...$ , where the digit $6$ repeats infinitely.
Convert the repeating decimal to a fraction: Convert the repeating decimal to a fraction. $\newline$ Let $x = 6.6666...$ $\newline$ Then, $10x = 66.6666...$ $\newline$ Subtract the first equation from the second equation to get rid of the repeating part: $\newline$ $10x - x = 66.6666... - 6.6666...$ $\newline$ $9x = 60$ $\newline$ $x = \frac{60}{9}$ $\newline$ $x = \frac{20}{3}$
Determine if the fraction is rational: Determine if the fraction is rational. $\newline$ The number $\frac{20}{3}$ is a fraction which represents a ratio of two integers ( $20$ and $3$ ), where the denominator is not zero. $\newline$ Therefore, $\frac{20}{3}$ is a rational number.