How do you convert 3.3 (3 repeating) as a fraction?

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Answer 1 · 2018-06-25T21:45:04

See a solution process below:

First, we can write:

$x = 3.bar3$

Next, we can multiply each side by $10$ giving:

$10x = 33.bar3$

Then we can subtract each side of the first equation from each side of the second equation giving:

$10x - x = 33.bar3 - 3.bar3$

We can now solve for $x$ as follows:

$10x - 1x = (33 + 0.bar3) - (3 + 0.bar3)$

$(10 - 1)x = 33 + 0.bar3 - 3 - 0.bar3$

$9x = (33 - 3) + (0.bar3 - 0.bar3)$

$9x = 30 + 0$

$9x = 30$

$(9x)/color(red)(9) = 30/color(red)(9)$

$(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = (3 xx 10)/color(red)(3 xx 3)$

$x = (color(red)(cancel(color(black)(3))) xx 10)/color(red)(color(black)(cancel(color(red)(3))) xx 3)$

$x = 10/3$