How to enter a repeating decimal in Mathematica

Question

I don't understand how to manipulate numbers with repeating decimal in Wolfram Mathematica language.

For example 0.3... does not work as input and I don't see how to add a vinculum to indicate the repeating part either. There's no manual or something on the issue on the net. Something strange and unusable 0.12(34)^_ (repeating decimal) is given by Wolfram Alpha.

Answer 1

Indeed, there is no direct method to input a repeating decimal. The closest you can get is to input the repeating digits into FromDigits[]:

$$0.\overline{142857}$$

FromDigits[{{{1, 4, 2, 8, 5, 7}}, 0}]
   1/7

$$0.\overline{3}$$

FromDigits[{{{3}}, 0}]
   1/3

$$0.1\overline{6}$$

FromDigits[{{1, {6}}, 0}]
   1/6

Of course, this also applies for e.g. repeating binary representations:

$${0.000\overline{1100}}_2$$

FromDigits[{{0, 0, 0, {1, 1, 0, 0}}, 0}, 2]
   1/10

Answer 2

Use the ResourceFunction RepeatingDecimalToRational:

ResourceFunction["RepeatingDecimalToRational"][0.3, 1]

(* 1/3 *)

Answer 3

I'm not sure if WolframAlpha notation is identical with Mathematica, although in the question you look like you used the 0.12343434... (3 dots), but in WolframAlpha (this is how I got to this question), you can use:

0.123434..

for 0.12(34)

WolframAlpha and Mathematica should be the same software under the covers having Steven Wolfram as creator. If not, I will let it as reference for those looking for WolframAlpha equivalent.