Express the rational number as a fraction of integers.
-$$0.0131131131 \ldots$$
A) $\frac { 131 } { 9900 }$
B) $\frac { 131 } { 999 }$
C) $\frac { 131 } { 9990 }$
D) $\frac { 131 } { 990 }$

Question

Quizplus · Accepted Answer

To express the repeating decimal $0.0131131131\ldots$ as a fraction, let $x = 0.0131131131\ldots$. Multiplying both sides by $10000$ (since the repeating part is four digits long), we get $10000x = 1311.31131\ldots$. Subtracting the original equation from this, $9999x = 1311.31131\ldots - 0.0131131131\ldots = 1311.2982$, we find $x = \frac{1311.2982}{9999}$. Simplifying this fraction by noticing that the numerator and denominator can be divided by their greatest common divisor, we get $x = \frac{131}{9990}$, which corresponds to option C.

Express the Rational Number as a Fraction of Integers 0.0131131131…0.0131131131 \ldots0.0131131131…

Express the Rational Number as a Fraction of Integers $0.0131131131 \ldots$