Answer: D) non-repeating, non-terminating decimal
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Step-by-step explanation:
Any rational number is of the form p/q, where p and q are integers and q is nonzero. So basically it's any fraction you can think of.
If a decimal terminates (ie stops) then it is a rational number.
For instance, 0.9 = 9/10 is rational
If a decimal repeats in some way, then it is rational
Eg: 0.0833333.... = 1/12
The dots after the 3 indicate the 3's go on forever.
So far, the facts mentioned allow us to rule out choices A and C. Choice B can be ruled out as well because any integer is always rational. We can easily prove it as such by writing the integer x as x/1.
A more concrete example could be writing the integer 7 as 7/1. So this shows 7 is rational and any integer is rational. Simply stick the integer over 1.
The only thing left at this point is choice D. Any non-repeating non-terminating decimal will be irrational. An example would be pi = 3.14159... which goes on forever without a pattern that repeats. Effectively the decimal digits of pi are more or less random. An irrational number is one that is not rational, and therefore cannot be written as a ratio of two integers.