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Which of the following are rational numbers? $\newline$ Multi-select Choices: $\newline$ (A) $0$ $\newline$ (B) $3.8$ $\newline$ (C) $10$ $\newline$ (D) $\pi$

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Classify numbers

Full solution

Q. Which of the following are rational numbers?

\newline

Multi-select Choices:

\newline

(A)

0

\newline

(B)

3.8

\newline

(C)

10

\newline

(D)

\pi

Define rational number: Step $1$ : Define a rational number. $\newline$ A rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. Rational numbers include integers, fractions, and terminating or repeating decimals.
Analyze choice (A): Step $2$ : Analyze choice (A) which is $0$ . $0$ can be expressed as $\frac{0}{1}$ , where $0$ is the numerator and $1$ is the denominator. Since both are integers and the denominator is not zero, $0$ is a rational number.
Analyze choice (B): Step $3$ : Analyze choice (B) which is $3.8$ . $3.8$ is a terminating decimal and can be expressed as $\frac{38}{10}$ , which simplifies to $\frac{19}{5}$ . Both $19$ and $5$ are integers, and the denominator is not zero, so $3.8$ is a rational number.
Analyze choice (C): Step $4$ : Analyze choice (C) which is $10$ . $10$ is an integer and can be expressed as $\frac{10}{1}$ . Since both $10$ and $1$ are integers and the denominator is not zero, $10$ is a rational number.
Analyze choice (D): Step $5$ : Analyze choice (D) which is $\pi$ (pi). $\newline$ $\pi$ is known to be an irrational number because it cannot be expressed as a fraction of two integers. Its decimal representation is non-terminating and non-repeating.

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