A non-repeating decimal, also known as a non-repeating decimal fraction, is a decimal number that does not have a repeating pattern of digits. Unlike repeating decimals, where a sequence of digits recurs indefinitely (like 0.333… or 0.142857142857…), a non-repeating decimal has digits that continue without repeating. An example of a non-repeating decimal is the number 0.123456789. Each digit is unique, and there is no group of digits that repeats.
Non-repeating decimals can be either finite or infinite. Finite non-repeating decimals terminate after a certain number of digits, such as 0.75, while infinite non-repeating decimals continue indefinitely without repeating patterns, such as the decimal expansion of the irrational number π (pi), which is approximately 3.14159…
In summary, non-repeating decimals are distinct due to their lack of repetitive sequences, and they can be found in both rational numbers (fractions that do not repeat) and irrational numbers (which do not terminate or repeat). Understanding these distinctions helps us navigate the world of numbers more effectively.