Convert 0.27¯¯¯¯¯ to a rational number in simplest form.(1 point)

Answer 1

To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can use a variable. Let x = 0.27¯¯¯¯¯.
Then, 100x = 27.¯¯¯¯¯
Now, we can subtract the two equations:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Dividing both sides by 99:
x = 27/99
This fraction can be further simplified. Both the numerator and the denominator are divisible by 9:
x = (27/9)/(99/9)
x = 3/11
Therefore, the rational number equivalent to 0.27¯¯¯¯¯ is 3/11 in simplest form.