Solve the problem.
-Rewrite the number $0 . \overline { 285 }$ as the quotient of two integers.
A) $\frac { 57 } { 200 }$
B) $\frac { 95 } { 333 }$
C) $\frac { 35 } { 111 }$
D) $\frac { 21 } { 200 }$

Question

Quizplus · Accepted Answer

To convert a repeating decimal to a fraction, you can use the formula $x = 0.\overline{abc}$ to get $1000x = abc.\overline{abc}$ and then subtract $x$ from $1000x$ to isolate the repeating part. For $0.\overline{285}$, let $x = 0.\overline{285}$, then $1000x = 285.\overline{285}$. Subtracting $x$ from $1000x$ gives $999x = 285$, so $x = \frac{285}{999}$. Simplifying this fraction gives $x = \frac{95}{333}$, which matches option B.

Solve the Problem 0.285‾0 . \overline { 285 }0.285 As the Quotient of Two Integers

Solve the Problem $0 . \overline { 285 }$ As the Quotient of Two Integers