Express the repeating decimal as a fraction in lowest terms.
-$0 . \overline { 72 }$
A) $\frac { 8 } { 11 }$
B) $\frac { 800 } { 11 }$
C) $\frac { 18 } { 25 }$
D) $\frac { 9 } { 125 }$

Question

Quizplus · Accepted Answer

To convert a repeating decimal to a fraction, let $x = 0.\overline{72}$. Multiplying both sides by 100 gives $100x = 72.\overline{72}$. Subtracting the original equation from this gives $99x = 72$, so $x = \frac{72}{99}$. Simplifying $\frac{72}{99}$ gives $\frac{8}{11}$.

Express the Repeating Decimal as a Fraction in Lowest Terms 0.72‾0 . \overline { 72 }0.72

Express the Repeating Decimal as a Fraction in Lowest Terms $0 . \overline { 72 }$