Question

Convert 0.09 (with a bar notation over 09) to a rational number in simplest form.

Answer 1

To convert a decimal number with a bar notation to a rational number in simplest form, we can follow these steps:

Let x = 0.090909...

Multiply x by 100 to remove the bar notation:
100x = 9.090909...

Subtract x from 100x:
100x - x = 9.090909... - 0.090909...
99x = 9

Divide both sides of the equation by 99:
x = 9/99

Simplify the fraction:
x = 1/11

Therefore, the rational number equivalent to 0.09 (with a bar notation over 09) in simplest form is 1/11.