Suppose that for a problem with solution $\mathrm{z}$, our approximated result was $\mathrm{z_0=175.002043}$ and the relative error committed $\mathrm{\frac{|\Delta z_0|}{|z|}} \le \mathrm{5x10^{-4}}$. Write the value of z.
As $\mathrm{z_0}$ has $\mathrm{9}$ significant digits, I could ensure that $\mathrm{\frac{|\Delta z_0|}{|z_0|}} \le \mathrm{5x10^{-9}}$, but how could I reach a value for z?
The fact that you are given more significant digits of $z_0$ than it makes sense with this relative error probably means that the excessive digits should be dropped, by rounding. So I assume that this problem is concerned with writing a quantity with error in the notation using $\pm$. In that case the conventions which I am used to dictate the following.
Find the absolute error and round it to a single significant digit (or two digits, if the first digit is $1$), so $|\Delta z_0|\approx 0.09$; round $z_0$ to the same precision as the rounded $|\Delta z_0|$, obtaining $175.00$; write down the answer as $z=175.00\pm0.09$.
If you didn't encounter anything like this before, then I probably misunderstood the assignment.