convert the following repeating decimal to a fraction in simplest form.\n.8\\overline{5}

Explanation:

Step1: Let ( x = 0.8\overline{5} )

Let ( x ) represent the repeating decimal. So ( x = 0.8555\ldots )

Step2: Multiply by 10 to shift non - repeating part

Multiply ( x ) by 10 to get ( 10x=8.555\ldots )

Step3: Multiply by 10 again to shift repeating part

Multiply ( 10x ) by 10 to get ( 100x = 85.555\ldots )

Step4: Subtract to eliminate repeating decimals

Subtract ( 10x ) from ( 100x ): ( 100x-10x=(85.555\ldots)-(8.555\ldots) ) ( 90x = 77 )

Step5: Solve for ( x )

Divide both sides by 90: ( x=\frac{77}{90} )

Answer:

(\frac{77}{90})