Convert to a Simplified Fraction 9.927083333

$9.92708\overline{3}$

Step 1

Set up an equation with $0.92708\overline{3}$ .

$x = 0.92708\overline{3}$

Step 2

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

Step 3

Multiply both sides of $x = 0.92708\overline{3}$ by $100000$ to create the first equation.

$100000 x = 92708.\overline{3}$

Step 4

Multiply both sides of $x = 0.92708\overline{3}$ by $1000000$ to create the second equation.

$1000000 x = 927083.\overline{3}$

Step 5

Subtract $100000 x = 92708.\overline{3}$ from $1000000 x = 927083.\overline{3}$ to remove the repeating part.

$900000 x = 834375$

Step 6

Divide each term in $900000 x = 834375$ by $900000$ and simplify.

Divide each term in $900000 x = 834375$ by $900000$ .

$\frac{900000 x}{900000} = \frac{834375}{900000}$

Simplify the left side.

Cancel the common factor of $900000$ .

Cancel the common factor.

$\frac{900000 x}{900000} = \frac{834375}{900000}$

Divide $x$ by $1$ .

$x = \frac{834375}{900000}$

Simplify the right side.

Cancel the common factor of $834375$ and $900000$ .

Factor $9375$ out of $834375$ .

$x = \frac{9375 (89)}{900000}$

Cancel the common factors.

Factor $9375$ out of $900000$ .

$x = \frac{9375 \cdot 89}{9375 \cdot 96}$

Cancel the common factor.

$x = \frac{9375 \cdot 89}{9375 \cdot 96}$

Rewrite the expression.

$x = \frac{89}{96}$

Step 7

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

$9 \frac{89}{96}$

Step 8

Convert $9 \frac{89}{96}$ to an improper fraction.

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

$9 + \frac{89}{96}$

Add $9$ and $\frac{89}{96}$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{96}{96}$ .

$9 \cdot \frac{96}{96} + \frac{89}{96}$

Combine $9$ and $\frac{96}{96}$ .

$\frac{9 \cdot 96}{96} + \frac{89}{96}$

Combine the numerators over the common denominator.

$\frac{9 \cdot 96 + 89}{96}$

Simplify the numerator.

Multiply $9$ by $96$ .

$\frac{864 + 89}{96}$

Add $864$ and $89$ .

$\frac{953}{96}$

Convert to a Simplified Fraction 9.927083333

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