How do you write #0.0545454...#, #54# repeating, as a fraction?

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Answer 1 · 2017-09-18T01:42:29

Think you want this as a fraction as it is already a decimal.

See a solution process below:

First, we can write:

#x = 0.0bar54#

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

#100x = 05.4bar54#

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

#100x - x = 5.4bar54 - 0.0bar54#

We can now solve for #x# as follows:

#100x - 1x = (5.4 + 0.0bar54) - 0.0bar54#

#(100 - 1)x = 5.4 + 0.0bar54 - 0.0bar54#

#99x = 5.4 + (0.bar054 - 0.0bar54)#

#99x = 5.4 + 0#

#99x = 5.4#

#(99x)/color(red)(99) = 5.4/color(red)(99)#

#(color(red)(cancel(color(black)(99)))x)/cancel(color(red)(99)) = (10 xx 5.4)/(10 xx 99)#

#x = 54/990#

#x = (18 xx 3)/(18 xx 55)#

#x = (color(red)(cancel(color(black)(18))) xx 3)/(color(red)(cancel(color(black)(18))) xx 55)#

#x = 3/55#