decimalendedness

Decimalendedness is a term used to describe the property of a number's decimal representation terminating after a finite number of digits. A number has decimalendedness if its fractional part can be expressed with a limited number of decimal places. For example, the number 0.5 is decimalended because it can be written as 5/10. Similarly, 0.25, which is 25/100, is also decimalended.

Conversely, numbers whose decimal representations do not terminate are considered to be non-decimalended. These numbers have an infinite number of decimal places that either repeat in a pattern (repeating decimals) or do not repeat at all (irrational numbers). Examples of non-decimalended numbers include 1/3, which results in the repeating decimal 0.333..., and pi (π), an irrational number with a non-repeating, infinite decimal expansion.

Mathematically, a rational number p/q (where p and q are integers and q is not zero) has decimalendedness if and only if the prime factors of the denominator q, after the fraction has been reduced to its lowest terms, consist only of 2s and 5s. If the denominator contains any prime factors other than 2 or 5, the decimal representation will be non-terminating. The concept is fundamental in understanding the nature of numbers and their representation in the decimal system.