Convert 0. overline 72 to a rational number in simplest form. (1 point)

Answer 1

To convert 0. overline 72 to a rational number in simplest form, we can use the formula for a repeating decimal. Let x = 0. overline 72.

To remove the repeating part, we multiply both sides of the equation by 100 to get 100x = 72.7272...

Next, we subtract the original equation from the equation with the repeating part removed:

100x - x = 72.7272... - 0. overline 72

99x = 72

Now, we can solve for x by dividing both sides of the equation by 99:

x = 72/99

To simplify the fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, which is 9.

Dividing both the numerator and denominator by 9 gives us the simplest form of the rational number:

x = (72/9)/(99/9) = 8/11

So, 0. overline 72 as a rational number in simplest form is 8/11.