0.83 * 100 = 83, so 0.83 = 83/100.
But in case you meant the slightly more interesting repeating decimal, 0.8333...:
Let <em>x</em> denote this number. Then
10<em>x</em> = 8.333...
100<em>x</em> = 83.333...
==> 100<em>x</em> - 10<em>x</em> = 83.333... - 8.333...
==> 90<em>x</em> = 83 - 8 = 75
==> <em>x</em> = 75/90 = 5/6
