Convert to a Simplified Fraction 0.782

$0.782$

Step 1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are

$3$ numbers to the right of the decimal point, place the decimal number over

$10^{3}$

$(1000)$ . Next, add the whole number to the left of the decimal.

$0 \frac{782}{1000}$

Step 2

Reduce the fraction.

Convert

$0 \frac{782}{1000}$ to an improper fraction.

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

$0 + \frac{782}{1000}$

Add

$0$ and

$\frac{782}{1000}$ .

$\frac{782}{1000}$

Cancel the common factor of

$782$ and

$1000$ .

Factor

$2$ out of

$782$ .

$\frac{2 (391)}{1000}$

Cancel the common factors.

Factor

$2$ out of

$1000$ .

$\frac{2 \cdot 391}{2 \cdot 500}$

Cancel the common factor.

$\frac{2 \cdot 391}{2 \cdot 500}$

Rewrite the expression.

$\frac{391}{500}$