Last month, a carpenter made 5 tableReasoning 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)
D. 4.443444… Real numbers are dense, meaning between any two numbers (rational or irrational), there will always be infinitely many others. Rational numbers are finite decimals or repeating decimals, but irrational ones never repeat or terminate. This ensures that irrational numbers fill the gaps between rationals, making the number line continuous. It shows why decimals like π or √2 cannot be expressed as fractions, unlike repeating decimals.
