Definition
Recurring decimal
A recurring decimal has a digit or finite block of digits that repeats forever.
What it means
Look for a repeating rhythm in the digits. The repeat might start straight away, as in 0.333…, or after some digits, as in 0.1666…. A bar or dots can show that the pattern continues without ending.
Remember it
Find the digit rhythm that never stops.
Example
2/11 = 0.181818…. The two-digit block 18 repeats forever, so the decimal is recurring.
Watch for
A displayed decimal such as 0.333 may be a rounded or cut-off value. The ellipsis, a bar, or an explicit statement of repetition is needed to show an endless repeat.
Common mix-up
0.333 is a terminating three-digit decimal; 0.333… is the exact recurring decimal equal to 1/3.
Exact meaning
A recurring decimal is a decimal expansion whose digits eventually enter a nonempty finite block that repeats forever. Every recurring decimal represents a rational number.