Question

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.

Which of the following distances are the same as 0.63 repeating of a mile?
1.)21/33
2.)9/11
3.)9/7
4.)63/100
5.)7/9
6.)7/11

Answer 1

Margie colored in the distance. 7/11 is the distances that is same as 0.63 repeating of a mile

Solution:

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=(63)/(99)=(7)/(11)} \\\\ {\text { Therefore, } 0.6363 \ldots=(7)/(11)}\end{array}`

Hence, the correct option is option 6.