Question

write the following decimal as a fraction of two integers in simplest form: $0.overline{66}$

Explanation:

Step1: Assign variable to decimal

Let $x = 0.\overline{66}$

Step2: Multiply by 100 to shift decimals

$100x = 66.\overline{66}$

Step3: Subtract original equation

$100x - x = 66.\overline{66} - 0.\overline{66}$
$99x = 66$

Step4: Solve for x

$x = \frac{66}{99}$

Step5: Simplify the fraction

$x = \frac{66\div33}{99\div33} = \frac{2}{3}$

Answer:

$\frac{2}{3}$