A rational, terminating decimal is a decimal that ends after a certain number of digits and can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator contains no prime factors other than 2 or 5.
Let's evaluate the options given:
-
79 - This is a rational number and can also be written as the decimal 79.0, which is terminating.
-
7 ninths (7/9) - This is a rational number but its decimal representation is 0.777..., which is repeating, not terminating.
-
0.363636... - This is a repeating decimal (it keeps repeating "36"), so it is not terminating.
-
511 - This is a rational number and can also be written as the decimal 511.0, which is terminating.
-
5 over 11 (5/11) - This is a rational number but its decimal representation is approximately 0.454545..., which is repeating, not terminating.
-
64−−√ (the square root of 64) - This equals 8, which is a rational number and can also be written as the decimal 8.0, which is terminating.
Based on this analysis, the options that are rational and terminating decimals are 79, 511, and 8 (or \( \sqrt{64} \)).
Since the question asks for just one answer, and pointing out that both 79 and 511 are terminating, you can choose either of these. If only selecting one option, 79 is a clear answer.