What is .4 repeating as a fraction?

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Mar 5, 2018

Answer:

See a solution process below:

Explanation:

First, we can write:

#x = 0.bar4#

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

#10x = 4.bar4#

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

#10x - x = 4.bar4 - 0.bar4#

We can now solve for #x# as follows:

#10x - 1x = (4 + 0.bar4) - 0.bar4#

#(10 - 1)x = 4 + 0.bar4 - 0.bar4#

#9x = 4 + (0.bar4 - 0.bar4)#

#9x = 4 + 0#

#9x = 4#

#(9x)/color(red)(9) = 4/color(red)(9)#

#(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 4/9#

#x = 4/9#

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