Which of the following best describes the nature of a repeating decimal?

A repeating decimal is a decimal number that has digits which repeat infinitely, such as 0.333... or 0.142857142857.... One of the key characteristics of repeating decimals is that they can be precisely represented as fractions. This is because any repeating decimal can be manipulated algebraically to form a fraction, demonstrating that it is a rational number.

For example, the repeating decimal 0.333... can be expressed as the fraction 1/3. Similarly, 0.142857142857... can be shown to equal 1/7. These conversions highlight that repeating decimals are not only irrational numbers, but rather they fit neatly within the category of rational numbers, which are both fractions and decimals.

Understanding this concept is essential for teaching, as it emphasizes the relationship between different forms of numbers and helps students grasp the properties of rational numbers.