Express the repeating decimal number as a quotient of two integers.
-$1.0 \overline { 76 }$
A) $\frac { 71 } { 660 }$
B) $\frac { 71 } { 66 }$
C) $\frac { 355 } { 33 }$
D) $\frac { 71 } { 33 }$

Question

Quizplus · Accepted Answer

To express $1.0\overline{76}$ as a quotient of two integers, let $x = 1.0\overline{76}$. Multiply $x$ by 100 to shift the repeating decimal two places to the left: $100x = 107.\overline{76}$. Subtract the original equation from this to eliminate the repeating part: $100x - x = 107.\overline{76} - 1.0\overline{76}$, which simplifies to $99x = 106.76$. Solving for $x$ gives $x = \frac{106.76}{99} = \frac{10676}{9900}$. Simplifying the fraction by dividing both the numerator and the denominator by 152 (the greatest common divisor) gives $x = \frac{71}{66}$.

Express the Repeating Decimal Number as a Quotient of Two 1.076‾1.0 \overline { 76 }1.076

Express the Repeating Decimal Number as a Quotient of Two $1.0 \overline { 76 }$