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

Answer 1

To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the method of converting repeating decimals to fractions.

Let x = 0.72¯¯¯¯¯

We can multiply both sides by 100 to eliminate the repeating decimal:

100x = 72.72¯¯¯¯¯

Now, we subtract the original equation from the equation above to eliminate the decimal part:

100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72

Dividing both sides by 99 gives us:

x = 72/99

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

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

Therefore, 0.72¯¯¯¯¯ as a rational number in simplest form is 8/11.