Question

Convert 0.533333... to a fraction. (only the 3 is repeating) Please show the work!!

Answer 1

Let x = 0.5333333333 ...

So 100x = 53.3333333333 ...
and 10x = 5.3333333333 ...
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90x = 53 – 5 = 48.

So x = 48/90 = 8/15 after reduction to lowest terms (by factor of 6)
0.3333... = ⅓. and that 0.5 = ½.

So 0.533333... = 0.5 + 0.0333333...0.5 + 0.3333.../10 = 1/2 + (1/3)/10 = 1/2 + 1/30 = 16/30 = 8/15