# Find the uncertainty in position

The question says:

A proton is accelerated to one tenth of the velocity of light. If it's velocity can be measured with a precision $$\pm 1\%$$. What must be its uncertainty in position?

Therefore,

$$v=0.1 \times c =3\cdot 10^7\ \pu{m/s}\\ \Delta(v)=\frac{1}{100}\\ m= 1.6\cdot10^{-27}\ \pu{kg}$$

Then I directly substituted these values into the formula: $$\Delta(v)\cdot\Delta(\text{position})\cdot \text{mass}=\frac h{4\pi}$$

To get the uncertainty in position, however, the answer I got was approx. $$3.5 \cdot 10^{-6}\ \pu{m}$$ which is way too different from the correct answer:

$$0.5\cdot10^{-13}\ \pu{m}.$$

Can anyone please explain me how to solve this question?