What is the product of $0.\overline{05}$ and $1.8$ expressed as a fraction in simplest form?

0.050505...... =  5/99 *1.8 =  [5/99] * [18/10]  = [5/10]*[18/99] = [ 1/2]*[18/99] = [9/99] = 1/11

As a fraction 0.05050505..... is 5/99

As a fraction 1.8 is 9/5

So the product is (5/99)*(9/5) = 1/11

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