How do you convert $3.8bar3$ (with a repeating $3$ ) to a fraction?

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Answer 1 · 2018-03-04T05:09:26

$3.8bar(3)=23/6 or 3 5/6$ .

Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical.

$100x=383.3333...$

$10x=38.3333...$

Subtracting the two equations, we have:

$90x=345$

So

$x=345/90$

$x=23/6 = 3 5/6$

How do you convert 3.8bar33.8bar3 (with a repeating 33) to a fraction?