First, there is no such thing as a terminating decimal - 1.5 is either 1.500... or 1.4999.... Let us, for the sake of convenience, use the form that ends in infinite zeroes.
If you have to go n decimal places into x before the infinite zeroes (a 'terminating' decimal), then you can mutiply x by 10^n/10^n and create a fraction where the numerator is an integer (by definition, you have moved all nonzero digits to the left of the decimale point) and the denominator is simply a power of ten (also an integer). Thus, rational number in all cases.
tl;dr: 'Terminating' decimals are actually repeating decimals. Repeating decimals can be written as fractions.
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Anonymous2007-01-30 4:43
No way Jose, they stop when I stop writing digits
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Anonymous2007-01-30 4:44
shorter version: by definition.
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Anonymous2007-01-30 5:51
>>4
An irrational number is defined as one that cannot be represented as a ratio of two integers. You have to make the connection for the OP, apparently.