You can identify a repeating number by examining the decimal portion of the number. Some repeating numbers are a single repeated digit. For example 0.33333. Other repeating numbers contain a more complex pattern, such as 0.285714285714285714. When you begin to see a pattern in the decimal portion of a number repeat, you know that the number is a repeating decimal number.
A repeating number results when you convert certain fractions to a decimal value. The fraction 1/3 converts to 0.3333333. The fraction 1/7 converts to 0.285714285714.
For repeating decimal numbers with a short repetition pattern, you can use one of three standard types of notation. You can draw a line over the repeating portion or under the repeating portion, or you can enclose the repeating portion in parentheses. For example: 0.333(3) or 0.285714(285714). For numbers with long repeating sequences, you can use the word "approximately" to identify the number as a repeating number or precede it with a tilde (~). For example, ~0.33333.
A repeating decimal number is not the same as an irrational number. An irrational number is one that never exhibits a repeating pattern, but instead infinitely produces a differing sequence of numbers as it becomes more precise. The most common example of an irrational number is pi (3.141592...).
A repeating decimal number can never be used in an exact calculation. In some calculations, it is acceptable to round the decimal portion of the number to a specific number of decimal places. When rounding a number, you truncate the portion after the decimal place you are rounding to. If the next number is 5 or greater, you add 1 to the last decimal place. For example, 0.3333333 rounded to the 1/1000th decimal place would be 0.333; whereas 0.285714(285714) rounded to the 1/1000th decimal place would be 0.286.