How do you convert 0.23 (3 repeating) as a fraction?

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Answer 1 · 2018-03-06T20:37:35

#7/30#

#0.23# with #3# repeating can be written as #0.2dot3#, where the dot on top of the #3# means a repeating number or pattern of numbers.

#x = 0.2dot3#

#10x = 2.dot3#

#100x=23.dot3#

#90x = 100x - 10x#

#90x = 23.dot3 - 2.dot3#

#90x = 23 - 2 = 21#

#90x = 21#

#x = 21/90#

#= 7/30#

Answer 2 · 2018-03-06T20:38:46

See a solution process below:

First, we can write:

#x = 0.2bar3#

Next, we can multiply each side by #10# giving:

#10x = 2.3bar3#

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

#10x - x = 2.3bar3 - 0.2bar3#

We can now solve for #x# as follows:

#10x - 1x = (2.3 + 0.0bar3) - (0.2 + 0.0bar3)#

#(10 - 1)x = 2.3 + 0.0bar3 - 0.2 - 0.0bar3#

#9x = (2.3 - 0.2) + (0.0bar3 - 0.0bar3)#

#9x = 2.1 + 0#

#9x = 2.1#

#(9x)/color(red)(9) = 2.1/color(red)(9)#

#(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 10/10 xx 2.1/color(red)(9)#

#x = 21/90#

#x = (3 xx 7)/(3 xx 30)#

#x = (color(red)(cancel(color(black)(3))) xx 7)/(color(red)(cancel(color(black)(3))) xx 30)#

#x = 7/30#