MATH SOLVE

2 months ago

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.