Convert to a Simplified Fraction 1.33333333

$1.\overline{3}$

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

Set up an equation with $1.\overline{3}$ .

$x = 1.\overline{3}$

Multiply both sides of $x = 1.\overline{3}$ by $10$ to create the second equation.

$10 x = 13.\overline{3}$

Subtract $x = 1.\overline{3}$ from $10 x = 13.\overline{3}$ to remove the repeating part.

$9 x = 12$

Divide each term by $9$ and simplify.

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Divide each term in $9 x = 12$ by $9$ .

$\frac{9 x}{9} = \frac{12}{9}$

Cancel the common factor of $9$ .

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Cancel the common factor.

$\frac{9 x}{9} = \frac{12}{9}$

Divide $x$ by $1$ .

$x = \frac{12}{9}$

Cancel the common factor of $12$ and $9$ .

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Factor $3$ out of $12$ .

$x = \frac{3 (4)}{9}$

Cancel the common factors.

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Factor $3$ out of $9$ .

$x = \frac{3 \cdot 4}{3 \cdot 3}$

Cancel the common factor.

$x = \frac{3 \cdot 4}{3 \cdot 3}$

Rewrite the expression.

$x = \frac{4}{3}$

The fractional form is the solution to the equation.

$\frac{4}{3}$

Convert to a Simplified Fraction 1.33333333

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