Question

write \\(\frac{8}{9}\\) as a decimal. if we continue to divide 8 by 9, the 8 will repeat forever. choose the decimal that’s equivalent to \\(\frac{8}{9}\\), \\(\

$$\begin{array}{r}0.888\\\\9\\overline{)8.000}\\\\-7.2\\downarrow\\\\\\hline.80\\\\-72\\downarrow\\\\\\hline.080\\\\-072\\\\\\hline.008\\end{array}$$

\\) 0.8 0.888 \\(0.\overline{8}\\)

Explanation:

Step1: Understand the division

When we divide 8 by 9, as shown in the long division, we keep getting a remainder that leads to the digit 8 repeating.

Step2: Identify the repeating decimal

The decimal equivalent of \(\frac{8}{9}\) is a repeating decimal where 8 repeats infinitely. The notation \(0.\overline{8}\) represents a decimal where 8 is repeating indefinitely. \(0.8\) is a terminating decimal (incorrect), \(0.888\) is a finite decimal (incorrect as the division shows it repeats), and \(0.\overline{8}\) is the correct repeating decimal.

Answer:

\(0.\overline{8}\)