Basic Math Examples

$0.\overline{629}$

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 $0.\overline{629}$ .

$x = 0.\overline{629}$

Step 3

Multiply both sides of $x = 0.\overline{629}$ by $1000$ to create the second equation.

$1000 x = 629.\overline{629}$

Step 4

Subtract $x = 0.\overline{629}$ from $1000 x = 629.\overline{629}$ to remove the repeating part.

$999 x = 629$

Step 5

Divide each term in $999 x = 629$ by $999$ and simplify.

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Step 5.1

Divide each term in $999 x = 629$ by $999$ .

$\frac{999 x}{999} = \frac{629}{999}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $999$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{999 x}{999} = \frac{629}{999}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{629}{999}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $629$ and $999$ .

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Step 5.3.1.1

Factor $37$ out of $629$ .

$x = \frac{37 (17)}{999}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $37$ out of $999$ .

$x = \frac{37 \cdot 17}{37 \cdot 27}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{37 \cdot 17}{37 \cdot 27}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{17}{27}$

Step 6

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

$0 \frac{17}{27}$

Step 7

Convert $0 \frac{17}{27}$ to an improper fraction.

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Step 7.1

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

$0 + \frac{17}{27}$

Step 7.2

Add $0$ and $\frac{17}{27}$ .

$\frac{17}{27}$