Express the number as the ratio of two integers.
-$1.818181 \ldots$
A) $18 \frac { 2 } { 11 }$
B) $1 \frac { 9 } { 11 }$
C) $1 \frac { 89 } { 111 }$
D) $\frac { 20 } { 111 }$

Question

Quizplus · Accepted Answer

Notice that the repeating block in the decimal representation is 81. Therefore, we can set up the equation $1.\overline{81}=\frac{x}{100}+\frac{81}{1100}$, where $x$ is the non-repeating part of the decimal. Solving for $x$ yields $x=\frac{100}{11}-\frac{81}{100}=\frac{9}{11}$. Thus, the number can be expressed as $\boxed{1\frac{9}{11}}$.

Express the Number as the Ratio of Two Integers 1.818181…1.818181 \ldots1.818181…

Express the Number as the Ratio of Two Integers $1.818181 \ldots$