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We think that the way to quickly find out if a fully simplified fraction, when converted into a decimal, is terminating or recurring is to check if the denominator’s prime factors are only 2 and 5. If there’s any other prime factor then it will not be a terminating decimal. This is as 2 and 5 are the only prime factors of 10, and since we use a number system of base 10 this makes them special. An example is ¾ 4 can be made by 2x2. Another example is 2/25 e.g 25/5=5 So, to see if it terminates, fully simplify it and then check if the denominators integers only prime factors are 2 and/or 5. If yes, then it terminates.