Full solution

Q. Which of the following are rational numbers?

\newline

Multi-select Choices:

\newline

(A)

3.8

\newline

(B)

4

\newline

(C)

1

\newline

(D)

6.333\ldots

Define Rational Number: Define what a rational number is. $\newline$ 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.
$3$ . $8$ is Rational: Determine if choice (A) $3.8$ is a rational number. $\newline$ $3.8$ is a terminating decimal because it has a finite number of digits after the decimal point. It can be expressed as the fraction $\frac{38}{10}$ , which is the quotient of two integers. Therefore, $3.8$ is a rational number.
$4$ is Rational: Determine if choice (B) $4$ is a rational number. $\newline$ $4$ is an integer, and all integers are rational numbers because they can be expressed as the quotient of themselves and $1$ (for example, $\frac{4}{1}$ ). Therefore, $4$ is a rational number.
$1$ is Rational: Determine if choice (C) $1$ is a rational number. $\newline$ $1$ is an integer, and as previously stated, all integers are rational numbers. Therefore, $1$ is a rational number.
$6.333\ldots$ is Rational: Determine if choice (D) $6.333\ldots$ is a rational number. $\newline$ $6.333\ldots$ is a repeating decimal because the digit $3$ repeats indefinitely. Repeating decimals are rational numbers because they can be expressed as a fraction. For example, $6.333\ldots$ can be expressed as the fraction $\frac{19}{3}$ . Therefore, $6.333\ldots$ is a rational number.