No, an element's atomic mass does not have infinite significant figures. The atomic mass of an element is a physical constant that represents the average mass of an atom of that element, taking into account the various isotopes and their relative abundances. The atomic mass is typically expressed in atomic mass units (amu) or unified atomic mass units (u).
The atomic mass of an element is determined experimentally and is subject to measurement uncertainties. Therefore, it is reported with a certain number of significant figures that reflect the precision of the measurement. The number of significant figures in the atomic mass depends on the accuracy of the experimental techniques used to determine it.
For example, the atomic mass of carbon is commonly stated as approximately 12.01 amu. The value "12.01" has four significant figures, indicating that the measurement is accurate to that degree of precision. This means that the actual atomic mass of carbon is known within a certain range of uncertainty, typically expressed as ±0.01 amu or ±0.02 amu, depending on the measurement technique.
In summary, an element's atomic mass is not infinite in terms of significant figures. It is a measured value with a finite number of significant figures that reflects the precision and accuracy of the experimental determination.