Which set of numbers does 4/7 belong to?

The number ( \frac{4}{7} ) is classified as a rational number because it can be expressed as the quotient of two integers, where the numerator (4) is an integer and the denominator (7) is a non-zero integer. In general, rational numbers include all numbers that can be written in the form ( \frac{a}{b} ), where ( a ) and ( b ) are integers and ( b ) is not zero.

Rational numbers encompass both terminating and repeating decimals, along with whole numbers and integers, as they can also be represented as fractions. Therefore, since ( \frac{4}{7} ) fits this definition, it is correctly identified as a rational number.

Other sets mentioned, like natural numbers, whole numbers, and real numbers, do not exclusively qualify ( \frac{4}{7} ). Natural numbers consist solely of positive integers like 1, 2, 3, etc. Whole numbers include all natural numbers as well as zero, and while ( \frac{4}{7} ) is a real number, the most accurate classification specific to its nature as a fraction is that it is a rational number.