We present low‐resolution turbulence profiles of the atmosphere above Dome C, Antarctica, measured with the MASS instrument during 25 nights in 2004 March–May. Except for the lowest layer, Dome C has significantly less turbulence than Cerro Tololo and Cerro Pachón. In particular, the integrated turbulence at 16 km is always less than the median values at the two Chilean sites. From these profiles we evaluate the photometric noise produced by scintillation, and the atmospheric contribution to the error budget in narrow‐angle differential astrometry. In comparison with the two midlatitude sites in Chile, Dome C offers a potential gain of about 3.6 in both photometric precision (for long integrations) and narrow‐angle astrometry precision. These gain estimates are preliminary, being computed with average wind‐speed profiles, but the validity of our approach is confirmed by independent data. Although the data from Dome C cover a fairly limited time frame, they lend strong support to expectations that Dome C will offer significant advantages for photometric and astrometric studies.