What is 0.27 repeated converted to a rational number in the simplest form

Answer 1

To convert 0.27 repeated to a rational number in simplest form, we can represent it as an infinite geometric series. Let x = 0.27 repeated.

x = 0.272727...
100x = 27.272727...

Now, subtract the two equations:

(100x - x) = (27.272727...) - (0.272727...)

99x = 27

To simplify, divide both sides by 99:

x = 27/99

The rational number in simplest form is 27/99, which can be further reduced by dividing both numerator and denominator by their greatest common divisor:

x = 3/11

Therefore, 0.27 repeated as a rational number in simplest form is 3/11.