How do you convert 0.8 (8 repeating) to a fraction?

Question

Lindsey Gamble · Accepted Answer

We have a decimal that repeats.,&amp;nbsp;0.8―&amp;nbsp;Let&#039;s adjust this to equal x.Then,&amp;nbsp;x=0.8―&amp;nbsp;Multiply both sides by 10:&amp;nbsp;10x=8.8―&amp;nbsp;This can be written&amp;nbsp;8.8―&amp;nbsp;when a whole number and a decimal number are added:10x=8+0.8―&amp;nbsp;Now, we know that&amp;nbsp;x=0.8―&amp;nbsp;10x=8+x&amp;nbsp;10x−x=8+x−x&amp;nbsp;9x=8&amp;nbsp;9x9=89&amp;nbsp;x=89&amp;nbsp;Therefore,&amp;nbsp;0.8―&amp;nbsp;0.8―=89

sonSnubsreose6v · Accepted Answer

The fractional value of 0.8 repeating is calculated by multiplying it by 10, which results in an 8 to the left of the decimal. This results in:
$x = 0.8888 \dots$
$10 x = 8.8888 \dots$
To find the value of x in our equations, we can now subtract these equations:
$10 x = 8.888 \dots$
$- x = 0.888 \dots$
Now that we know the value of x, we can divide both sides by 9.
$9 x = 8$
$\frac{9 x}{9} = \frac{8}{9}$
$x = \frac{8}{9}$

How do you convert 0.8 (8 repeating) to a fraction?

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