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That's because all repeating decimals can be converted into fractions. Here is an example: 4.161616... Let's call this number "x". Multiply by 100 (use a "1" followed by two zeroes in this case, because the repetition period is two), and write:
100x = 416.161616...
x = 4.161616...
Subtract the two equations:
99x = 412
x = 412 / 99
So there you have it - the number was converted to a fraction made up of integers - which is exactly the definition of "rational number".
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All repeating decimals are rational numbers?
Yes.
Are all terminating and repeating decimals rational numbers Explain?
Yes, they are.
What is the set of all integers plus all of the termination or repeating decimals?
The rational numbers
Are all nonterminating decimals irrational numbers?
Not at all. 0.33333... nonterminating = 1/3 rational 0.66666... nonterminating = 2/3 rational 0.1428571428... nonterminating = 1/7 rational 0.55555... nonterminating = 5/9 rational
Are all terminating and decimals rational numbers?
All terminating decimal numbers are rational.
