Question 989509
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It already is a rational number.  Any decimal number with a repeating pattern is rational.  What I think you meant to ask, or what your instructor meant to ask is to express *[tex \Large 0.\overline{4}] as a quotient of integers.


Let *[tex \Large a\ =\ 0.\overline{4}].  Then *[tex \Large 10a\ =\ 4.\overline{4}].
<pre>
     10a  =  4.4...
    -  a  =  0.4...
    ---------------
      9a  =  4.0...
</pre>
Hence *[tex \Large a\ =\ \frac{4}{9}]


Commit these to memory:  1 ninth is 0.111..., 2 ninths is 0.222..., and so on.    


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \