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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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Q: Why are all repeating decimals rational numbers?
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