What is 0.194 as a fraction with the 9 and 4 going forever? (its basically 0.194949494..., but instead its written with the forever bar on top)

Question

Baically, the 9 and 4 go on forever. If the entire decimal went on forever, this would be much easier because I actually learned how to solve that in school, but I haven't learned this. 

Answer 1

Did you know that the decimal approximation of any ninth is that digit repeated?

For example, 1/9≈0.111111 and 2/9≈0.222222222

 

We can use that with two-digit numbers also, so 94/99≈0.94949494

 

Except we don't want the tenths column to contain that pattern. We can shift the entire pattern to the right one place by dividing by a number ten times as large. Try entering 94/990 into a calculator...

 

But in this case, we want to start with a one in the tenths column. That's equal to one tenth, or 1/10.

 

We want 1/10 and 94/990 .... if we add 1/10 + 94/990 = 99/990 + 94/990 = 193/990

Answer 2

Let x = 0.194949494....

Can you calculate the value of 1000x?

Can you calculate the value of 10x?

 

What is the value of 1000x - 10x?

 

This should help you find the fraction - by solving for x.

 

I started with multiplying by 1000 so that one occurrence of the repeating decimal ends up on the left side of the decimal point. You might have done a similar problem in school without that 1 being there and not repeating.