Margie colored in the distance. 7/11 is the distances that is same as 0.63 repeating of a mile
<u>Solution:</u>
Given that, Margie colored in the distance from her best friend's house to her house and wrote on the map that the distance was 0.63 repeating of a mile.
we have to find Which of the following distances are the same as 0.63 repeating of a mile?
We let 0.63 (63 being repeated) be x.
x=0.6363...
Since x is recurring in 2 decimal places, we multiply it by 100.
100x=63.6363...
Next, we subtract them.
100x−x=63.6363...−0.6363...
99x=63
The recurring digits '63' cancel off and the result is that 99x is non-recurring.
Lastly, we divide both sides by 99 to get x as a fraction.
![\begin{array}{l}{x=\frac{63}{99}=\frac{7}{11}} \\\\ {\text { Therefore, } 0.6363 \ldots=\frac{7}{11}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Bx%3D%5Cfrac%7B63%7D%7B99%7D%3D%5Cfrac%7B7%7D%7B11%7D%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Therefore%2C%20%7D%200.6363%20%5Cldots%3D%5Cfrac%7B7%7D%7B11%7D%7D%5Cend%7Barray%7D)
Hence, the correct option is option 6.