Step 1: Pick the right rule.
When we are not sure about both speed and position of a tiny particle, we use the Heisenberg uncertainty principle: $\Delta x\cdot \Delta p\geq \frac{h}{4\pi}$.
Step 2: Bring in the mass.
Momentum is mass times speed, so $\Delta p=m\,\Delta v$. Putting this in gives $\Delta x\geq \frac{h}{4\pi m\,\Delta v}$.
Step 3: Find the uncertainty in speed.
The speed is $x$ and it is known within $0.001\%$. So \[ \Delta v=x\times\frac{0.001}{100}=x\times10^{-5}\ \text{m/s} \]
Step 4: Put every value in.
With $m=9\times10^{-31}$ kg and $h=6.6\times10^{-34}$ Js: \[ \Delta x=\frac{6.6\times10^{-34}}{4\pi(9\times10^{-31})(x\times10^{-5})} \]
Step 5: Tidy the powers of ten.
The denominator constants give $4\times9=36$ and $10^{-31}\times10^{-5}=10^{-36}$. So \[ \Delta x=\frac{6.6\times10^{-34}}{36\pi\,x\times10^{-36}}=\frac{6.6\times10^{2}}{36\pi x}=\frac{660}{36\pi x} \]
Step 6: Reduce the fraction.
Divide top and bottom by 12: $\frac{660}{36}=\frac{55}{3}$. \[ \boxed{\Delta x=\dfrac{55}{3\pi x}\ \text{m}} \]