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

Answer 1

To convert the repeating decimal 0.72¯¯¯¯¯¯ to a rational number in simplest form, we have to set up an equation.

Let x = 0.72¯¯¯¯¯¯

Then 100x = 72.72¯¯¯¯¯¯

Subtracting the first equation from the second equation, we get:

100x - x = 72.72¯¯¯¯¯¯ - 0.72¯¯¯¯¯¯

99x = 72

Dividing both sides of the equation by 99, we get:

x = 72/99

To simplify the fraction 72/99, we can divide both the numerator and denominator by their greatest common divisor, which is 9:

x = (72 ÷ 9) / (99 ÷ 9)
= 8/11

Therefore, the rational number equivalent of 0.72¯¯¯¯¯¯ is 8/11.