The relation between the units and the readings of time and space coordinates of the terrestrial and the barycentric frames is discussed from the viewpoint of general relativity. Attention is paid to the unit of space coordinates since the International Astronomical Union (IAU) regulates only the unit of time coordinate in the above two frames. Two definitions on unit of length are examined and their effects on the numerical expression of coordinate transformation, equations of planetary motions, and those for light propagation time are discussed. A clear conflict is found between the IAU(1976) recommendation on the definition of the time-scales in different frames and the statement that all constants in the IAU(1976) new system of astronomical constants are defined in terms of the international system of units (SI units). In order to dissolve this conflict, one of the two examined definitions on unit of length is proposed to be adopted, which requests the least alteration on the current procedures to analyze the astrometric observations such as radar/laser rangings, range and range-rate measurements, and very long baseline interferometric observations. An interpretation of numerical values in the IAU(1976) system of astronomical constants is also presented. It is stressed that the definition proposed in this paper requires that a slightly different formula from the current one be used in the numerical transformation of coordinates between the terrestrial and the barycentric frames.