Precise measurement of physical quantities underpins much of modern science and tech- nology. Examples include length and time (satellite navigation), rotation and acceleration (guidance systems), electromagnetic (magnetic resonance imaging) and gravitational fields (mineral exploration). Currently, precision measurement of many physically and practically interesting quantities - such as the fine structure constant, the local gravitational field or any inertial acceleration - can be accomplished by atom interferometry [1]. Using cold atom interferometers may enable yet more precision, but this precision will be limited by atomic shot noise. Atomic shot noise, which is a fluctuation in the atomic density, arises because atoms are discrete. This fluctuation will affect precision when counting the atoms in a cloud, as is done in atomic interferometry. In this thesis, atomic shot noise was clearly and quantitatively measured in cold rubidium 87 atomic clouds using the absorption imaging technique. This was achieved by minimizing all possible sources of classical noise from the imaging setup, then binning the pixels together to overcome blurring effects. These blurring effects can be due to the velocity distribution of the atoms, the diffraction limit of the optical system, and the photon recoil in the measurement process itself. The tantalising possibility exists of measuring the shot noise on a Bose-Einstein condensate, and thereby gaining information on its quantum statistics. A scheme to produce and measure squeezing (a reduction in variance beyond the shot noise limit) in an atom laser beam will require a detector capable of measuring at the atomic shot noise limit, like the one devel- oped in this thesis. At the moment, applying this technique to measuring the shot noise on a BEC is limited by the size of the condensate and the resolution of the imaging system, but in principle it should be possible, as this thesis demonstrates. A full calibration of the experimental setup is performed.The application of this work to increasing the precision of cold atom interferometry is discussed.