To convert the decimal 0.72¯¯¯¯¯ to a rational number, we can assign it the variable x and express it as an equation:
x = 0.72¯¯¯¯¯
To eliminate the recurring bar, we can multiply both sides of the equation by a power of 10 that will move the decimal point to the right of the recurring bar. In this case, we can multiply by 1000:
1000x = 720.72¯¯¯¯¯
Now we can subtract the original equation from this new equation to eliminate the recurring bar:
1000x - x = 720.72¯¯¯¯¯ - 0.72¯¯¯¯¯
999x = 720
To express x as a rational number, we divide both sides of the equation by 999:
x = 720/999
To simplify this, we find the greatest common divisor (GCD) of 720 and 999, which is 9. We can divide the numerator and denominator by 9:
x = (720/9)/(999/9)
x = 80/111
So, 0.72¯¯¯¯¯ is equal to 80/111 in simplest form.
Regarding the statement that 8/11 is the correct answer, it is incorrect. The correct answer is 80/111, as shown above.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
explain how 8/11 is the correct answer
1 answer