## terminating decimal

### A terminating decimal is a decimal number that can be written as a finite number of digits after the decimal point

A terminating decimal is a decimal number that can be written as a finite number of digits after the decimal point. In other words, it is a decimal that has an end and does not continue indefinitely. In a terminating decimal, the digits after the decimal point eventually stop or terminate.

For example, the decimal representation of the fraction 1/4 is 0.25, which is a terminating decimal because it has two digits after the decimal point and then stops. Other examples of terminating decimals include 0.8, -3.14, and 7.0.

It is important to note that not all decimals are terminating. For instance, the decimal representation of the fraction 1/3 is 0.3333…, where the digit 3 repeats infinitely. This repeating decimal does not have an end and is considered non-terminating.

To determine if a fraction will result in a terminating decimal when expressed as a decimal, you can look at its prime factorization. If the denominator of the fraction has only 2s or 5s (or both) in its prime factorization, the resulting decimal will be terminating. For example, 1/8 = 0.125 is terminating because the denominator (8) only has 2s in its prime factorization. On the other hand, if the denominator has a prime factor other than 2 or 5, the resulting decimal will be non-terminating. For example, 1/3 = 0.3333… is non-terminating because the denominator (3) has a prime factor of 3.

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