The simplified fraction is [tex]\frac{25}{3 }[/tex].
Solution:
Given expression:
[tex]3.8 \overline{3}[/tex]
[tex]3.8 \overline{3}=8.33333...[/tex]
Let x = 8.33333... -------- (1)
Multiply by 10 on both sides.
10x = 83.3333... -------- (2)
Subtract (1) from (2),
10x - x = 83.3333... - 8.33333...
9x = 75
Divide by 7 on both sides, we get
[tex]$x=\frac{75}{9}[/tex]
[tex]$x=\frac{25\times 3}{3 \times 3}[/tex]
Cancel the common factor 3.
[tex]$x=\frac{25}{3 }[/tex]
[tex]$ 3.8 \overline{3}=\frac{25}{3 }[/tex]
Hence the simplified fraction is [tex]\frac{25}{3 }[/tex].
