Express the repeating decimal as a fraction in lowest terms.
-$0 . \overline { 468 }$
A) $\frac { 52 } { 111 }$
B) $\frac { 166 } { 333 }$
C) $\frac { 117 } { 250 }$
D) $\frac { 83 } { 500 }$

Question

Quizplus · Accepted Answer

To convert a repeating decimal to a fraction, let $x = 0.\overline{468}$. Multiply $x$ by 1000 to shift the decimal three places to the right, getting $1000x = 468.\overline{468}$. Subtract $x$ from $1000x$ to eliminate the repeating part: $999x = 468$, which simplifies to $x = \frac{468}{999}$. Simplifying this fraction gives $\frac{52}{111}$.

Express the Repeating Decimal as a Fraction in Lowest Terms 0.468‾0 . \overline { 468 }0.468

Express the Repeating Decimal as a Fraction in Lowest Terms $0 . \overline { 468 }$