Question

Rewrite as a simplified fraction.

Answer 1

The simplified fraction is $\frac{25}{3 }$.

Solution:

Given expression:

$3.8 \overline{3}$

$3.8 \overline{3}=8.33333...$

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

$x=\frac{75}{9}$

$x=\frac{25\times 3}{3 \times 3}$

Cancel the common factor 3.

$x=\frac{25}{3 }$

$3.8 \overline{3}=\frac{25}{3 }$

Hence the simplified fraction is $\frac{25}{3 }$.