To write [tex]\(3.\overline{7}\)[/tex] (3.7777...) as a mixed number, follow these steps:
1. Let [tex]\( x = 3.\overline{7} \)[/tex]:
[tex]\[
x = 3.777777\ldots
\][/tex]
2. Multiply [tex]\( x \)[/tex] by 10:
[tex]\[
10x = 37.777777\ldots
\][/tex]
3. Subtract [tex]\( x \)[/tex] from [tex]\( 10x \)[/tex]:
[tex]\[
10x - x = 37.777777\ldots - 3.777777\ldots
\][/tex]
[tex]\[
9x = 34
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{34}{9}
\][/tex]
So, the mixed number representation of [tex]\(3.\overline{7}\)[/tex] is:
[tex]\[
3.\overline{7} = \frac{34}{9}
\][/tex]
