Convert to a Simplified Fraction -2.48148148

$- 2.\overline{481}$

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

$0.\overline{481}$ .

$x = 0.\overline{481}$

Step 3

Multiply both sides of

$x = 0.\overline{481}$ by

$1000$ to create the second equation.

$1000 x = 481.\overline{481}$

Step 4

Subtract

$x = 0.\overline{481}$ from

$1000 x = 481.\overline{481}$ to remove the repeating part.

$999 x = 481$

Step 5

Divide each term in

$999 x = 481$ by

$999$ and simplify.

Divide each term in

$999 x = 481$ by

$999$ .

$\frac{999 x}{999} = \frac{481}{999}$

Simplify the left side.

Cancel the common factor of

$999$ .

Cancel the common factor.

$\frac{999 x}{999} = \frac{481}{999}$

Divide

$x$ by

$1$ .

$x = \frac{481}{999}$

Simplify the right side.

Cancel the common factor of

$481$ and

$999$ .

Factor

$37$ out of

$481$ .

$x = \frac{37 (13)}{999}$

Cancel the common factors.

Factor

$37$ out of

$999$ .

$x = \frac{37 \cdot 13}{37 \cdot 27}$

Cancel the common factor.

$x = \frac{37 \cdot 13}{37 \cdot 27}$

Rewrite the expression.

$x = \frac{13}{27}$

Step 6

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

$- 2 \frac{13}{27}$

Step 7

Convert

$2 \frac{13}{27}$ to an improper fraction.

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

$- (2 + \frac{13}{27})$

Add

$2$ and

$\frac{13}{27}$ .

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{27}{27}$ .

$- (2 \cdot \frac{27}{27} + \frac{13}{27})$

Combine

$2$ and

$\frac{27}{27}$ .

$- (\frac{2 \cdot 27}{27} + \frac{13}{27})$

Combine the numerators over the common denominator.

$- \frac{2 \cdot 27 + 13}{27}$

Simplify the numerator.

Multiply

$2$ by

$27$ .

$- \frac{54 + 13}{27}$

Add

$54$ and

$13$ .

$- \frac{67}{27}$

Convert to a Simplified Fraction -2.48148148

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