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Which of the following are rational numbers?\newlineMulti-select Choices:\newline(A) 3.83.8\newline(B) 44\newline(C) 11\newline(D) 6.333…6.333\ldots

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Q. Which of the following are rational numbers?\newlineMulti-select Choices:\newline(A) 3.83.8\newline(B) 44\newline(C) 11\newline(D) 6.333…6.333\ldots
  1. Define Rational Number: Define what a rational number is.\newlineA rational number is a number that can be expressed as the quotient or fraction pq\frac{p}{q} of two integers, where pp and qq are integers and q≠0q \neq 0. Rational numbers include terminating decimals and repeating decimals.
  2. 33.88 is Rational: Determine if choice (A) 3.83.8 is a rational number.\newline3.83.8 is a terminating decimal because it has a finite number of digits after the decimal point. It can be expressed as the fraction 3810\frac{38}{10}, which is the quotient of two integers. Therefore, 3.83.8 is a rational number.
  3. 44 is Rational: Determine if choice (B) 44 is a rational number.\newline44 is an integer, and all integers are rational numbers because they can be expressed as the quotient of themselves and 11 (for example, 41\frac{4}{1}). Therefore, 44 is a rational number.
  4. 11 is Rational: Determine if choice (C) 11 is a rational number.\newline11 is an integer, and as previously stated, all integers are rational numbers. Therefore, 11 is a rational number.
  5. 6.333…6.333\ldots is Rational: Determine if choice (D) 6.333…6.333\ldots is a rational number.\newline6.333…6.333\ldots is a repeating decimal because the digit 33 repeats indefinitely. Repeating decimals are rational numbers because they can be expressed as a fraction. For example, 6.333…6.333\ldots can be expressed as the fraction 193\frac{19}{3}. Therefore, 6.333…6.333\ldots is a rational number.

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