To determine the fractional form of the repeating decimal [tex]\( 0.\overline{8} \)[/tex], follow these steps:
1. Let the repeating decimal be represented by [tex]\( x \)[/tex]:
[tex]\[
x = 0.\overline{8}
\][/tex]
2. Express the repeating decimal by multiplying [tex]\( x \)[/tex] by 10:
[tex]\[
10x = 8.8888\ldots
\][/tex]
Here, the decimal part is again [tex]\( 0.\overline{8} \)[/tex].
3. Subtract the original equation from this new equation:
[tex]\[
10x = 8.8888\ldots
\][/tex]
[tex]\[
- (x = 0.8888\ldots)
\][/tex]
[tex]\[
9x = 8
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{8}{9}
\][/tex]
Thus, the fractional form of [tex]\( 0.\overline{8} \)[/tex] is:
[tex]\[
\frac{8}{9}
\][/tex]
The correct answer is:
C. [tex]\(\frac{8}{9}\)[/tex]
