How do you convert $0.$ $dot4$ $dot7$ to a fraction?

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Answer 1 · 2017-07-02T07:36:07

$47/99$

Let's take your value, $0.$ $dot4$ $dot7$ , as a variable such that:
$r=0.$ $dot4$ $dot7$

Since the $47$ infinityly repeats itself, we can easily cancel it:
If $r=0.$ $dot4$ $dot7$ , then $100r=47.$ $dot4$ $dot7$

$99r=100r-r= 47.$ $dot4$ $dot7-0.$ $dot4$ $dot7$ $=47$ .

Now you have $99r=47$ , divide both sides to find $r$ :
$99r=47$
$r=47/99=0.$ $dot4$ $dot7$

How do you convert 0.0.dot4dot4dot7dot7 to a fraction?