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 can follow these steps:

Step 1: Assign a variable to the original repeating decimal:
Let x = 0.72¯¯¯¯¯

Step 2: Multiply both sides of the equation by 100 (to move the decimal point two places to the right):
100x = 72.72¯¯¯¯¯

Step 3: Subtract the original equation from the newly multiplied equation to eliminate the repeating part:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72

Step 4: Divide both sides of the equation by 99 to solve for x:
x = 72/99

Step 5: Simplify the resulting fraction if possible:
The fraction 72/99 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = 8/11

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