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

Question

42790 views around the world

You can reuse this answer
Creative Commons License

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#