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#