How can a measurment be both precise and accurate?

Accuracy refers to the closeness of a value to a known or standard value, while precision refers to the closeness of measurements (two or more) to each other. 

The best way to remember how to distinguish between the two definitions and apply them is to think of archery. The archer's goal is to be both accurate and precise. To do this, he/she must try and shoot each arrow as close to the middle and as close to each other as possible. If the archer's arrows landed all over the target, these shots would be neither accurate nor precise. If the arrows landed closely to each other, but far away from the middle, these shots would be considered precise, but not accurate. If the arrows all landed closely to each other AND in the middle, the shots would be BOTH accurate and precise.

So, if you consistently measured values that were close to each other, and were close to the accepted/known value, then your measurements would be both accurate and precise. 

I hope this helps you.