What is .4 repeating as a fraction?

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Answer 1 · 2018-03-05T02:35:46

See a solution process below:

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:

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

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

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

$9x = 4 + 0$

$9x = 4$

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

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

$x = 4/9$