Question

What is 3.25 with the 5 repeating as a rational number

Answer 1

322 over 99 is your answer. Hope this helps!

Answer 2

So,

$3.2\overline{5}$

Multiply it by 100.

$3.2\overline{5}--\ \textgreater \ 325.5\overline{5}$.

We now know that $325.5\overline{5}$ is 100 times of $3.2\overline{5}$.  If we subtract the first from the second, we will get 99 of the number.  Then, we can simply divide by 99 and we will have it in fraction form.

$325.5\overline{5}-3.2\overline{5}=322.3$

Now, we put it over 99.

$\frac{322.3}{99}$

Of course, we cannot have decimals in fraction form, so we will just fix that.

$\frac{3223}{990}= \frac{11*293}{2*3*3*5*11}=\frac{293}{2*3*3*5}=\frac{293}{90}\ or\ 3 \frac{23}{90}$