Convert 0.2727.... to a rational number in simplest form. (1 point)

Answer 1

Let x = 0.2727...
10x = 2.7272...

Now, subtract the first equation from the second equation to eliminate the repeating part:

10x - x = 2.7272... - 0.2727...
9x = 2.4545...

Dividing both sides by 9:

x = 2.4545... / 9

To simplify the fraction, we can express 2.4545... as a fraction:

Let y = 2.4545...
100y = 245.4545...

Now, subtract the first equation from the second equation to eliminate the repeating part:

100y - y = 245.4545... - 2.4545...
99y = 243

Dividing both sides by 99:

y = 243 / 99

Simplifying the fraction:

y = 3

Therefore, x = 2.4545... / 9 simplifies to x = 243 / 99 in simplest form.