How do you convert 0.21 (21 repeating) as a fraction?

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Answer 1 · 2017-08-29T22:32:11

See a solution process below:

First:

Let $x = 0.bar21$

Then let, $100x = 21.bar21$

We can now subtract each side of the first equation from each side of the second equation and solve for $x$ :

$100x - x = 21.bar21 - 0.bar21$

$100x - 1x = (21 + 0.bar21) - 0.bar21$

$(100 - 1)x = 21 + 0.bar21 - 0.bar21$

$99x = 21 + 0$

$99x = 21$

$(99x)/color(red)(99) = 21/color(red)(99)$

$(color(red)(cancel(color(black)(99)))x)/cancel(color(red)(99)) = (3 xx 7)/color(red)(3 xx 33)$

$x = (color(red)(cancel(color(black)(3))) xx 7)/color(red)(color(black)(cancel(color(red)(3))) xx 33)$

$x = 7/33$

$0.bar21 = 7/33$