Convert to a Simplified Fraction 0.777777777777

$0.\overline{7}$

Step 1

Create two equations where the only numbers to the right of the decimal place are the repeating part.

Step 2

Set up an equation with

$0.\overline{7}$ .

$x = 0.\overline{7}$

Step 3

Multiply both sides of

$x = 0.\overline{7}$ by

$10$ to create the second equation.

$10 x = 7.\overline{7}$

Step 4

Subtract

$x = 0.\overline{7}$ from

$10 x = 7.\overline{7}$ to remove the repeating part.

$9 x = 7$

Step 5

Divide each term in

$9 x = 7$ by

$9$ and simplify.

Divide each term in

$9 x = 7$ by

$9$ .

$\frac{9 x}{9} = \frac{7}{9}$

Simplify the left side.

Cancel the common factor of

$9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{7}{9}$

Divide

$x$ by

$1$ .

$x = \frac{7}{9}$

Step 6

Write as a mixed number by taking the whole number part along with the solution to the equation.

$0 \frac{7}{9}$

Step 7

Convert

$0 \frac{7}{9}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$0 + \frac{7}{9}$

Add

$0$ and

$\frac{7}{9}$ .

$\frac{7}{9}$