What is 0.31 (31 repeating) as a fraction?

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Answer 1 · 2018-06-20T18:34:56

See a solution process below:

First, we can write:

#x = 0.bar31#

Next, we can multiply each side by #100# giving:

#100x = 31.bar31#

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

#100x - x = 31.bar31 - 0.bar31#

We can now solve for #x# as follows:

#100x - 1x = (31 + 0.bar31) - 0.bar31#

#(100 - 1)x = 31 + 0.bar31 - 0.bar31#

#99x = 31 + (0.bar31 - 0.bar31)#

#99x = 31 + 0#

#99x = 31#

#(99x)/color(red)(99) = 31/color(red)(99)#

#(color(red)(cancel(color(black)(99)))x)/cancel(color(red)(99)) = 31/99#

#x = 31/99#