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Which of the following are real numbers?\newlineMulti-select Choices:\newline(A) 1010\newline(B) 910\frac{9}{10}\newline(C) 1.4441.444\ldots\newline(D) 3\sqrt{3}

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Q. Which of the following are real numbers?\newlineMulti-select Choices:\newline(A) 1010\newline(B) 910\frac{9}{10}\newline(C) 1.4441.444\ldots\newline(D) 3\sqrt{3}
  1. Real Numbers Definition: Real numbers include all the numbers on the number line, including all rational and irrational numbers. Rational numbers are those that can be expressed as a fraction of two integers, ab\frac{a}{b}, where aa and bb are integers and b0b \neq 0, and irrational numbers cannot be expressed as a simple fraction.
  2. 1010 as a Real Number: (A) 1010 is a whole number, which is also a rational number because it can be expressed as a fraction (101\frac{10}{1}). Therefore, it is a real number.
  3. ext{99/1010 as a Real Number:} (B) 910\frac{9}{10} is a fraction, which is a rational number. All rational numbers are real numbers.
  4. 11.444444... as a Real Number: (C) 1.4441.444\ldots (where the dots indicate that the number is repeating) is a repeating decimal, which is also a rational number. Therefore, it is a real number.
  5. 3\sqrt{3} as an Irrational Real Number: (D) 3\sqrt{3} or the square root of 33 is an irrational number because it cannot be expressed as a simple fraction. However, irrational numbers are also real numbers.

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