Determine if 0, point, 7, 4, 7, 4, 4, 7, 4, 4, 4, 7, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 7, point, point, .0.747447444744447444447... is rational or irrational and give a reason for your answer.

Answer 1

To determine if the number is rational or irrational, we need to analyze the pattern of digits.

The given number starts with 0 and then repeats the sequence 7, 4, 4, 4, 7 multiple times. This pattern continues indefinitely.

If we examine the repeating portion, it consists of the digits 7 and 4, which are both integers. Since the repeating portion consists of integers, we can deduce that the number is rational.

Therefore, the number 0.747447444744447444447... is rational.