Convert to a Simplified Fraction 36.36363636

$36.\overline{36}$

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 $0.\overline{36}$ .

$x = 0.\overline{36}$

Step 3

Multiply both sides of $x = 0.\overline{36}$ by $100$ to create the second equation.

$100 x = 36.\overline{36}$

Step 4

Subtract $x = 0.\overline{36}$ from $100 x = 36.\overline{36}$ to remove the repeating part.

$99 x = 36$

Step 5

Divide each term in $99 x = 36$ by $99$ and simplify.

Divide each term in $99 x = 36$ by $99$ .

$\frac{99 x}{99} = \frac{36}{99}$

Simplify the left side.

Cancel the common factor of $99$ .

Cancel the common factor.

$\frac{99 x}{99} = \frac{36}{99}$

Divide $x$ by $1$ .

$x = \frac{36}{99}$

Simplify the right side.

Cancel the common factor of $36$ and $99$ .

Factor $9$ out of $36$ .

$x = \frac{9 (4)}{99}$

Cancel the common factors.

Factor $9$ out of $99$ .

$x = \frac{9 \cdot 4}{9 \cdot 11}$

Cancel the common factor.

$x = \frac{9 \cdot 4}{9 \cdot 11}$

Rewrite the expression.

$x = \frac{4}{11}$

Step 6

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

$36 \frac{4}{11}$

Step 7

Convert $36 \frac{4}{11}$ to an improper fraction.

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

$36 + \frac{4}{11}$

Add $36$ and $\frac{4}{11}$ .

To write $36$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$36 \cdot \frac{11}{11} + \frac{4}{11}$

Combine $36$ and $\frac{11}{11}$ .

$\frac{36 \cdot 11}{11} + \frac{4}{11}$

Combine the numerators over the common denominator.

$\frac{36 \cdot 11 + 4}{11}$

Simplify the numerator.

Multiply $36$ by $11$ .

$\frac{396 + 4}{11}$

Add $396$ and $4$ .

$\frac{400}{11}$

Convert to a Simplified Fraction 36.36363636

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