convert 0.27... to a rational number in the simplest form

Answer 1

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.