Full solution

Q. Which of the following are real numbers?

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Multi-select Choices:

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(A)

9

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(B)

\pi

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(C)

7.78

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(D)

2

Define Real Numbers: Define what a real number is. $\newline$ A real number is any number that can be found on the number line. This includes both rational numbers (such as integers, fractions, and terminating or repeating decimals) and irrational numbers (numbers that cannot be expressed as a simple fraction, such as $\sqrt{2}$ or $\pi$ ).
ext{ extdollar} $9$ ext{ extdollar} is a Real Number: Determine if choice (A) ext{ extdollar} $9$ ext{ extdollar} is a real number. $\newline$ ext{ extdollar} $9$ ext{ extdollar} is an integer, and all integers are real numbers because they can be located on the number line.
ext{ extpi ext{ is a Real Number:}} Determine if choice (B) ext{ extpi ext{ ( extpi)}} is a real number. $\newline$ ext{ extpi ext{ is an irrational number because it cannot be expressed as a simple fraction, and its decimal representation is non-terminating and non-repeating. However, irrational numbers are also real numbers because they can be located on the number line.}}
$7$ . $78$ is a Real Number: Determine if choice (C) $7.78$ is a real number. $\newline$ $7.78$ is a terminating decimal, and all terminating decimals represent rational numbers. Rational numbers are real numbers because they can be located on the number line.
ext{ extdollar{} $2$ extdollar{} is a Real Number:} Determine if choice (D) ext{ extdollar{} $2$ extdollar{}} is a real number. $\newline$ ext{ extdollar{} $2$ extdollar{}} is an integer, and as previously stated, all integers are real numbers because they can be located on the number line.