Convert 0.27¯¯¯¯¯0.27¯ to a rational number in simplest form.(1 point) Responses 311 Start Fraction 3 over 11 end fraction 27100 Start Fraction 27 over 100 end fraction 127 Start Fraction 1 over 27 end fraction 2799

Answer 1

To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we can let x = 0.27¯¯¯¯¯ and multiply both sides of the equation by 100 to eliminate the repeating decimal:

100x = 27.¯¯¯¯¯

Now, we can subtract x from both sides of the equation:

100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯

99x = 27

To express as a fraction, we can write:

99x = 27

Dividing both sides of the equation by 99, we get:

x = 27/99

Simplifying the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:

x = 27/99 = (27/9)/(99/9) = 3/11

Therefore, 0.27¯¯¯¯¯ is equal to 3/11 in simplest form. Hence, the correct option is Start Fraction 3 over 11 end fraction.