Question

What is 0.8333 forever in a fraction

Answer 1

$x=0.8\overline{3}\\ 10x=8.\overline{3}\\ 100x=83.\overline{3}\\\\ 100x-10x=83.\overline{3}-8.\overline{3}\\ 90x=75\\ x=\dfrac{75}{90}=\dfrac{5}{6}$

Answer 2

There are a couple of different approaches you can use for this. Here's one.

1. Determine how many digits repeat. (There is just one repeating digit.)

2. Call your number x. Multiply x by 10 to the power of the number of digits found in step 1.

$x = 0.8\overline{3}\\10^{1}x=8.3\overline{3}$

3. Subtract the original number, then solve for x.

$10x-x=9x=8.3\overline{3}-0.8\overline{3}=7.5\\\\x=\dfrac{7.5}{9}=\dfrac{5}{6}$

_____

If you recognize that 0.333... (repeating) is 1/3, then you know that 0.0333... (repeating) is 1/10×1/3 = 1/30. Add that to 0.8 = 4/5 and you get

... 4/5 + 1/30 = 24/30 + 1/30 = 25/30 = 5/6