Question

What fraction is equivalent to 0.34⎯⎯⎯⎯0.34¯. Show or explain how you found your answer.

Answer 1

We know that

Two fractions are equivalent only if the product of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other 
that means
a/b=c/d-------> a*d=c*b

so

0.34=0.34/1=34/100---------> 0.34/1=34/100
then
0.34*100=1*34-------> 34=34------> fractions (0.34/1) and (34/100) are equivalent

34/100-------> 17//50
34*50=100*17---------> 1700=1700-----> fractions 34/100 and 17/50 are equivalent

the answer is
17/50