The number 0.666... represents a repeating decimal where the digit 6 continues indefinitely. It can be expressed as a fraction, specifically \frac23. This means that if you divide 2 by 3, you will get 0.666... as the result, illustrating that repeating decimals can often be converted into simpler fractional forms. In mathematics, repeating decimals like 0.666... are important because they show how certain numbers can be represented in different ways. Understanding these conversions helps in grasping concepts related to fractions, decimals, and rational numbers, which are foundational in arithmetic and algebra.