A repeating decimal is a decimal number that has a digit or a group of digits that repeat infinitely. For example, the fraction 1/3 can be expressed as the decimal 0.333..., where the digit "3" continues indefinitely. This type of decimal can also be represented with a bar notation, such as 0.3̅. Repeating decimals can arise from dividing integers, particularly when the denominator has prime factors other than 2 or 5. They are important in mathematics because they illustrate the relationship between fractions and decimals, helping to understand concepts like rational numbers.