Convert 0.09¯¯¯¯¯ to a rational number in simplest form

Answer 1

To convert the repeating decimal 0.09¯¯¯¯¯ to a rational number, we can set it equal to the variable x and multiply both sides of the equation by 100 to remove the repeating decimal.

0.09¯¯¯¯¯ = x

Multiplying both sides by 100 gives:

100(0.09¯¯¯¯¯) = 100x

9.¯¯¯¯¯ = 100x

Now, let's subtract the original equation from the above equation:

100x - x = 9.¯¯¯¯¯ - 0.09¯¯¯¯¯

99x = 9

Dividing both sides by 99, we get:

x = 9/99

Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, we get:

x = 1/11

Therefore, the rational number equivalent to 0.09¯¯¯¯¯ is 1/11.