(2) What is \( 0 . \overline{5} \) in fraction form?
(A) \( \frac{1}{2} \)
(B) \( \frac{1}{5} \)
(C) \( \frac{5}{9} \)
(D) \( \frac{5}{10} \)

Answer

Expert–verified

Hide Steps

Answer

Compute the sum of the geometric series: x = \( \frac{5}{9} \)

Steps

Step 1 ：Let x = \( 0 . \overline{5} \)

Step 2 ：Write the decimal as a geometric series: x = \( 5(\frac{1}{10} + \frac{1}{100} + \frac{1}{1000} + ...) \)

Step 3 ：Compute the sum of the geometric series: x = \( \frac{5}{9} \)