Determine if 0.292992999299992999992...is a rational or irrational and give a reason for your answer.
To determine if the number 0.292992999299992999992... is rational or irrational, we need to analyze its pattern.
Looking closely at the decimal representation, we can observe that after the first digit (0), the number 2 repeats every three digits (the sequence "929" repeats), and the number 9 repeats every six digits (the sequence "929929" repeats).
In general, a number is rational if and only if its decimal representation either terminates or repeats in a pattern. In this case, we have established that the decimal does repeat in a pattern, which implies that 0.292992999299992999992... is a rational number.
Thus, the number 0.292992999299992999992... is rational.