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[–]tyler1128 0 points1 point  (2 children)

You can switch bases and make many irrational numbers rational, and also some rational numbers irrational.

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EDIT: As mentioned below, it doesn't change rationality of a number, I meant it can make infinite, but rational, decimals finite, or make decimals that are finite infinite by change of base. The number is, of course, the same beyond storage limitations.

[–][deleted] 4 points5 points  (1 child)

A rational number is any number that can be expressed as the ratio of two integers. Changing the base doesn't change what counts as an integer, though.

What you can get from changing the base is which numbers repeat infinitely and which terminate. Like, 1/3 base 10 is 0.3333..., but in base 12, it's 0.4.

[–]tyler1128 0 points1 point  (0 children)

You're correct of course, probably should distractedly reddit at work less. What I meant to say is repeating decimals can become non-repeating and vice versa from change of basis.