In mathematics, the term "terminating" is often used to describe a type of decimal representation of a number. Specifically, a decimal is considered terminating if it has a finite number of digits after the decimal point. For example, the numbers 0.5, 1.75, and 3.0 are all terminating decimals because they have a definite end.
In contrast, a non-terminating decimal does not have a finite number of digits after the decimal point. Non-terminating decimals can be further classified into two categories: repeating (or recurring) decimals, which have a repeating pattern (like 1/3 = 0.333... or 0.666...), and non-repeating decimals, which do not have a repeating pattern (like the decimal expansion of π or the square root of 2).
A rational number (a number that can be expressed as a fraction of two integers) will have a terminating decimal representation if, after simplification, the denominator has only the prime factors 2 and/or 5. For example, the fraction 1/8 has a terminating decimal representation (0.125), while 1/3 does not (it equals 0.333...).
In summary, a terminating decimal is one with a finite number of decimal places, while other forms of decimal representations can be non-terminating either through repetition or non-repeating patterns.
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