Question

repeating decimals are irrational or rational

Answer 1

Repeating decimals are considered rational numbers. A rational number is any number that can be expressed as the quotient or fraction of two integers (where the denominator is not zero). Repeating decimals can always be written as a fraction, which is why they are classified as rational.

For example, the decimal \(0.333...\) (where the 3 repeats indefinitely) can be expressed as the fraction \(\frac{1}{3}\), and \(0.666...\) can be expressed as \(\frac{2}{3}\). In general, any decimal that has a repeating pattern can be converted to a fraction, confirming its status as a rational number.