convert 0.27... to a rational number in the simplest form
To convert the repeating decimal 0.27... to a rational number, we need to find a fraction that is equal to this decimal.
Let x = 0.27...
To eliminate the repeating part, we can multiply x by 100:
100x = 27.27...
Now we can subtract x from 100x:
100x - x = 27.27... - 0.27...
Simplifying:
99x = 27
Dividing both sides by 99:
x = 27/99
This fraction can be simplified to its simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 3:
x = 9/33
Further simplification can be done by dividing both the numerator and denominator by their greatest common divisor, which is 3:
x = 3/11
So, 0.27... is equal to the rational number 3/11 in its simplest form.