convert 0.72 ̅ to a rational number in simplest form

Answer 1

To convert the recurring decimal 0.72 ̅ to a rational number in simplest form, we need to express it as a fraction.

Let x = 0.72 ̅

To remove the recurring decimal, let's multiply both sides of the equation by 10:

10x = 7.2 ̅

Now, we can subtract the original equation from this new equation:

10x - x = 7.2 ̅ - 0.72 ̅

Simplifying the right side:

9x = 7.2

Now, divide both sides by 9:

9x/9 = 7.2/9

x = 0.8

Therefore, 0.72 ̅ as a rational number in simplest form is 0.8.