Express the repeating decimal as a fraction in lowest terms.
-$0 . \overline { 77 } = \frac { 77 } { 100 } + \frac { 77 } { 10,000 } + \frac { 77 } { 1,000,000 } + \ldots$
A) $\frac { 7777 } { 10000 }$

B) $\frac { 7777 } { 999 }$

C) $\frac { 7 } { 9 }$

D) $\frac { 7700 } { 999 }$

Question

Express the repeating decimal as a fraction in lowest terms.
-$0 . \overline { 77 } = \frac { 77 } { 100 } + \frac { 77 } { 10,000 } + \frac { 77 } { 1,000,000 } + \ldots$
A) $\frac { 7777 } { 10000 }$

B) $\frac { 7777 } { 999 }$

C) $\frac { 7 } { 9 }$

D) $\frac { 7700 } { 999 }$

Quizplus · Accepted Answer

To express $0.\overline{77}$ as a fraction, let $x = 0.\overline{77}$. Multiplying both sides by 100 gives $100x = 77.\overline{77}$. Subtracting the original equation from this, $99x = 77$, so $x = \frac{77}{99} = \frac{7}{9}$.

Express the Repeating Decimal as a Fraction in Lowest Terms 0.77‾=77100+7710,000+771,000,000+…0 . \overline { 77 } = \frac { 77 } { 100 } + \frac { 77 } { 10,000 } + \frac { 77 } { 1,000,000 } + \ldots0.77=10077​+10,00077​+1,000,00077​+…

Express the Repeating Decimal as a Fraction in Lowest Terms $0 . \overline { 77 } = \frac { 77 } { 100 } + \frac { 77 } { 10,000 } + \frac { 77 } { 1,000,000 } + \ldots$