Reasoning The numbers 4.333 . . . and 4.444 . . . are both rational numbers. Which of the following is an irrational number that is between these two rational numbers? Use pencil and paper. Show why there has to be an irrational number between any two rational numbers. 5.334333 . . . 4.443444 . . . 4.334 4.334333 . . . Question content area bottom Part 1 Which of the following is an irrational number that is between the two rational numbers? Select all that apply. A. 4.334333 . . . B.4.334 4.334 C. 5.334333 . . . D. 4.443444 . . .
Answer (1)
The answer is D. 4.443444… Rational numbers either terminate or repeat. Irrational numbers do not terminate or repeat. Since option D is a non-repeating decimal within the range, it is irrational. This proves that no matter how close two rational numbers are, there will always be at least one irrational number between them. This is a key concept in real number theory.
