Write the rational number $0 . \overline { 81 }$ as the quotient of two integers in simplest form.
A) $\frac { 9 } { 11 }$
B) $\frac { 4 } { 11 }$
C) $\frac { 5 } { 11 }$
D) $\frac { 10 } { 11 }$
E) $\frac { 8 } { 11 }$

Question

Quizplus · Accepted Answer

To convert the repeating decimal $0.\overline{81}$ to a fraction, let $x = 0.\overline{81}$. Multiply both sides by 100 (since there are two repeating digits) to get $100x = 81.\overline{81}$. Subtract the original equation from this to eliminate the repeating part: $100x - x = 81.\overline{81} - 0.\overline{81}$, which simplifies to $99x = 81$. Solving for $x$ gives $x = \frac{81}{99}$, which simplifies to $\frac{9}{11}$ when both numerator and denominator are divided by their greatest common divisor, 9.

Write the Rational Number 0.81‾0 . \overline { 81 }0.81 As the Quotient of Two Integers in Simplest Form

Write the Rational Number $0 . \overline { 81 }$ As the Quotient of Two Integers in Simplest Form