How do you convert 0.8 (8 repeating) to a fraction?

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Answer 1 · 2016-06-07T16:25:04

$0.bar8=8/9$

We have a repeating decimal, $0.bar8$

Let us put this equal to $x$ .

Then,

$x=0.bar8$

Multiply both sides by $10$ :

$10x=8.bar8$

We can write this $8.bar8$ as a sum of a whole number and a decimal number:

$10x=color(red)(8)+color(blue)(0.bar8)$

Now, we know that $x=0.bar8$

$10x=8+x$

$10xcolor(red)(-x)=8+xcolor(red)(-x)$

$9x=8$

$(9x)/color(red)(9)=8/color(red)(9)$

$x=8/9$

Therefore,

$0.bar8=8/9$