Question

Convert 0.72¯¯¯¯¯ to a rational number in simplest form. please.

Answer 1

To convert 0.72¯¯¯¯¯ to a rational number, we can use the infinite geometric series formula.

Let x = 0.72¯¯¯¯¯
Multiply both sides of the equation by 100:
100x = 72.7272¯¯¯¯¯

Subtract the original equation from the modified one:
100x - x = 72.7272¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72

Divide both sides of the equation by 99:
x = 72/99

The fraction 72/99 can be simplified by finding the greatest common divisor (GCD) of 72 and 99, which is 9. Dividing both the numerator and denominator by 9:
x = (72/9) / (99/9)
x = 8/11

Therefore, 0.72¯¯¯¯¯ is equivalent to the rational number 8/11 in simplest form.