Is the following number rational or irrational? 0. bar(7) Choose 1 answer: (A) Rational (B) Irrational

Evaluate the meaning: Evaluate the meaning of 0. bar(7). 0. bar(7) means 0.777777..., where the digit 7 repeats indefinitely.Set up an equation: Set up an equation to represent 0. bar(7). Let x = 0. bar(7).Multiply both sides: Multiply both sides of the equation by 10 to shift the decimal point one place to the right. 10x = 7. bar(7).Subtract the original equation: Subtract the original equation (x = 0. bar(7)) from the new equation (10x = 7. bar(7)) to get rid of the repeating decimals. 10x - x = 7. bar(7) - 0. bar(7).Perform the subtraction: Perform the subtraction to find the value of 9x. 9x = 7Divide both sides: Divide both sides by 9 to solve for x. x = 7/9Identify whether: Identify whether 7/9 is a rational or irrational number. 7/9 is a fraction which represents a ratio of two integers, therefore it is a rational number.Conclude that: Conclude that 0. bar(7) is a rational number because it can be expressed as the fraction 7/9.

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Is the following number rational or irrational?

0. bar(7)
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational? $\newline$ $0.\overline{7}$ $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational

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Algebra 2

Classify rational and irrational numbers

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Q. Is the following number rational or irrational?

\newline

0.\overline{7}

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

Evaluate the meaning: Evaluate the meaning of $0.\overline{7}$ . $\newline$ $0.\overline{7}$ means $0.777777\ldots$ , where the digit $7$ repeats indefinitely.
Set up an equation: Set up an equation to represent $0.\overline{7}$ . $\newline$ Let $x = 0.\overline{7}$ .
Multiply both sides: Multiply both sides of the equation by $10$ to shift the decimal point one place to the right. $\newline$ $10x = 7.\overline{7}.$
Subtract the original equation: Subtract the original equation $(x = 0.\overline{7})$ from the new equation $(10x = 7.\overline{7})$ to get rid of the repeating decimals. $\newline$ $10x - x = 7.\overline{7} - 0.\overline{7}$ .
Perform the subtraction: Perform the subtraction to find the value of $9x$ . $9x = 7$
Divide both sides: Divide both sides by $9$ to solve for $x$ . $\newline$ $x = \frac{7}{9}$
Identify whether: Identify whether $\frac{7}{9}$ is a rational or irrational number. $\newline$ $\frac{7}{9}$ is a fraction which represents a ratio of two integers, therefore it is a rational number.
Conclude that: Conclude that $0.\overline{7}$ is a rational number because it can be expressed as the fraction $\frac{7}{9}$ .