Is the following number rational or irrational? 0. bar(151) Choose 1 answer: (A) Rational (B) Irrational

Represent as fraction: Let's represent 0. bar(151) as a fraction to see if it's rational or not. Let x = 0.151151151...Multiply by 1000: Multiply x by 1000 to shift the decimal three places to the right: 1000x = 151.151151...Subtract original x: Subtract the original x from 1000x to get rid of the repeating decimals: 1000x - x = 151.151151... - 0.151151...Simplify to x = 151/999: This gives us 999x = 151, which simplifies to x = 151/999.Conclusion: x is rational: Since we can express x as a fraction (151/999), it means x is a rational number.

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Is the following number rational or irrational?

0. bar(151)
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational? $\newline$ $0.\overline{151}$ $\newline$ 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{151}

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

Represent as fraction: Let's represent $0.\overline{151}$ as a fraction to see if it's rational or not. Let $x = 0.151151151\ldots$
Multiply by $1000$ : Multiply $x$ by $1000$ to shift the decimal three places to the right: $1000x = 151.151151\ldots$
Subtract original x: Subtract the original $x$ from $1000x$ to get rid of the repeating decimals: $1000x - x = 151.151151... - 0.151151...$
Simplify to $x = \frac{151}{999}$ : This gives us $999x = 151$ , which simplifies to $x = \frac{151}{999}$ .
Conclusion: $x$ is rational: Since we can express $x$ as a fraction ( $\frac{151}{999}$ ), it means $x$ is a rational number.