What is a terminating decimal?

A terminating decimal is a decimal number that contains a finite number of digits after the decimal point. In other words, it ends. There's no infinitely repeating sequence of digits.

Here's some key information:

• Representation: Terminating decimals can be expressed as a fraction where the denominator is a power of 10 (10, 100, 1000, etc.). For example, 0.75 can be written as 75/100, and 0.125 can be written as 125/1000.

• Fraction Form: A fraction will produce a terminating decimal only if its denominator, in simplest form (after canceling common factors from the numerator and denominator), contains only the prime factors 2 and/or 5 (or none at all). For instance, 3/8 (8 = 2³) terminates, as does 7/20 (20 = 2² x 5), but 1/3 does not because its denominator is 3.

• Conversion to Fraction: Converting a terminating decimal to a fraction involves placing the digits after the decimal point over a power of 10 corresponding to the number of digits. Then, simplify the fraction. Example: 0.375 = 375/1000 = 3/8

• Contrast with Repeating Decimals: Repeating decimals, on the other hand, have a sequence of digits that repeat infinitely. For example, 1/3 = 0.3333... This is fundamentally different from a terminating decimal.

In short, terminating decimals are a subset of the rational numbers (numbers that can be expressed as a fraction of two integers) that have a particularly simple and finite decimal representation.