Is9.333...arationalnumber? Choices: (A)yes (B)no

Definition of Rational Number: Understand the definition of a rational number. A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where p and q are integers and q is not zero. Rational numbers include terminating decimals and repeating decimals.Analysis of 9.333...: Analyze the number 9.333... The number 9.333... has a repeating decimal. The three dots indicate that the digit '3' repeats indefinitely.Expressing 9.333... as a Fraction: Determine if 9.333... can be expressed as a fraction. Since 9.333... is a repeating decimal, it can be expressed as a fraction. To do this, let x = 9.333... Then, 10x = 93.333... Subtracting the original number from this, we get 10x - x = 93.333... - 9.333..., which simplifies to 9x = 84. Therefore, x = 84/9, which can be simplified to x = 28/3.Conclusion: Rational Number: Conclude whether 9.333... is a rational number. Since we have expressed 9.333... as the fraction 28/3, it is a rational number.

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Is $9.333\ldots$ a rational number? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Q. Is

9.333\ldots

a rational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Definition of Rational Number: Understand the definition of a rational number. A rational number is a number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where $p$ and $q$ are integers and $q \neq 0$ . Rational numbers include terminating decimals and repeating decimals.
Analysis of $9.333\ldots$ : Analyze the number $9.333\ldots$ $\newline$ The number $9.333\ldots$ has a repeating decimal. The three dots indicate that the digit ' $3$ ' repeats indefinitely.
Expressing $9.333\ldots$ as a Fraction: Determine if $9.333\ldots$ can be expressed as a fraction. $\newline$ Since $9.333\ldots$ is a repeating decimal, it can be expressed as a fraction. To do this, let $x = 9.333\ldots$ Then, $10x = 93.333\ldots$ Subtracting the original number from this, we get $10x - x = 93.333\ldots - 9.333\ldots$ , which simplifies to $9x = 84$ . Therefore, $x = \frac{84}{9}$ , which can be simplified to $x = \frac{28}{3}$ .
Conclusion: Rational Number: Conclude whether $9.333\ldots$ is a rational number. $\newline$ Since we have expressed $9.333\ldots$ as the fraction $\frac{28}{3}$ , it is a rational number.