Final answer:
Dan is mistaken because the non-terminating, repeating decimal of 1/7 still represents a rational number as it can be expressed as a fraction.
Step-by-step explanation:
Dan is mistaken because a rational number is defined as a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. The fact that 1 divided by 7 (1/7) results in a non-terminating decimal does not make it irrational. Rather, because this decimal is repeating (0.142857...), it still represents a rational number. Non-terminating decimals that are repeating represent rational numbers because they can be written as a fraction.