The triple point of water is defined to take place at 273.16 K, where K is the SI unit Kelvin. Unlike Celsius and Fahrenheit scales, Kelvin is not measured using degrees; we merely say "Kelvin."
The triple point of water is important enough to merit its own line:
T3 = 273.1K
This is equivalent to 0.01oC and 32.02oF, and thus we use T3 to help set the freezing point of water.
Absolute zero is defined as being equivalent to that of 0 Kelvin, which is -273.15oC and and -459.67oF, and this is a standard that is accepted internationally. It is important to note that the pressure the triple point exists at is 4.58 torr in SI units or .006 atm. To compare, the Earth's average atmospheric pressure is 1 atm.