Convert to a Simplified Fraction 0.83333333

$0.8\overline{3}$

Set up an equation with $0.8\overline{3}$ .

$x = 0.8\overline{3}$

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

Multiply both sides of $x = 0.8\overline{3}$ by $10$ to create the first equation.

$10 x = 8.\overline{3}$

Multiply both sides of $x = 0.8\overline{3}$ by $100$ to create the second equation.

$100 x = 83.\overline{3}$

Subtract $10 x = 8.\overline{3}$ from $100 x = 83.\overline{3}$ to remove the repeating part.

$90 x = 75$

Divide each term by $90$ and simplify.

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Divide each term in $90 x = 75$ by $90$ .

$\frac{90 x}{90} = \frac{75}{90}$

Cancel the common factor of $90$ .

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Cancel the common factor.

$\frac{90 x}{90} = \frac{75}{90}$

Divide $x$ by $1$ .

$x = \frac{75}{90}$

Cancel the common factor of $75$ and $90$ .

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Factor $15$ out of $75$ .

$x = \frac{15 (5)}{90}$

Cancel the common factors.

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Factor $15$ out of $90$ .

$x = \frac{15 \cdot 5}{15 \cdot 6}$

Cancel the common factor.

$x = \frac{15 \cdot 5}{15 \cdot 6}$

Rewrite the expression.

$x = \frac{5}{6}$

The fractional form is the solution to the equation.

$\frac{5}{6}$

Convert to a Simplified Fraction 0.83333333

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