Q:

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.)21/332.)9/113.)9/74.)63/1005.)7/96.)7/11

Accepted Solution

A:
Margie colored in the distance. 7/11 is the distances that is same as 0.63 repeating of a mileSolution: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. [tex]\begin{array}{l}{x=\frac{63}{99}=\frac{7}{11}} \\\\ {\text { Therefore, } 0.6363 \ldots=\frac{7}{11}}\end{array}[/tex]Hence, the correct option is option 6.