Final answer:
Nathaniel is correct; the number is rational because it is a fraction. All fractions are rational as they represent the division of two integers, and a rational number in decimal form must either terminate or repeat.
Step-by-step explanation:
To determine which boy is correct between Ronald and Nathaniel, we need to explore the definition of a rational number. A rational number is any number that can be expressed as the quotient or fraction a/b of two integers, where a is the numerator and b (the denominator) is not zero. It is important to note that for a number to be rational, when it is in decimal form, it must either terminate (ends after a finite number of digits) or repeat (has a repeating pattern of digits).
Nathaniel is correct that the number is rational because it is a fraction. All fractions are rational by definition because they represent the division of two integers. Ronald’s assertion that the number is not rational based solely on the fact that its decimal form does not terminate is incorrect. If the decimal has a repeating pattern, the number is also rational. For example, 1/3 equals 0.333..., which does not terminate but is still a rational number because of the repeating set of digits.
In conclusion, a fraction is always a rational number, regardless of whether its decimal representation terminates or not, as long as if it does not terminate, it repeats. Since all fractions meet these criteria, they are always considered rational numbers.