Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar. Answer correctly, don't make no errors!
The decimal representation of 8/11 is 0.72 with a repeating digit of 7. Therefore, the expression can be written as 0.72¯¯¯¯¯¯.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, let's assign a variable to it. Let x = 0.72¯¯¯¯¯.
To remove the repeating bar, we multiply both sides of the equation by 100 (since there are two decimal places after the decimal point):
100x = 72.72¯¯¯¯¯
Now, let's subtract x from both sides:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
Simplifying both sides:
99x = 72
Dividing both sides by 99:
x = 72/99
To simplify the fraction, we can find the greatest common divisor (GCD) of the numerator and the denominator, which is 9. Dividing both the numerator and denominator by 9:
x = (72 ÷ 9) / (99 ÷ 9)
x = 8/11
Therefore, the rational number equivalent to the repeating decimal 0.72¯¯¯¯¯ is 8/11 in simplest form.