Question

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

Answer 1

To convert 0.72¯¯¯¯¯ to a rational number, we can set it equal to a variable, say x:
x = 0.72¯¯¯¯¯
Multiply both sides of the equation by 100 to remove the repeating decimal:
100x = 72.72¯¯¯¯¯
Subtract the original equation from the new equation to eliminate the repeating decimal:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Divide both sides of the equation by 99 to solve for x:
x = 72/99
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which in this case is 9:
x = (72/9)/(99/9)
x = 8/11
Therefore, 0.72¯¯¯¯¯ is equal to the rational number 8/11 in simplest form.