If you look at the periodic table, you will notice that most elements have atomic masses that are not whole numbers. Chlorine, for instance, has an atomic mass of 35.45 amu — not 35, not 36, but something in between. This is not a measurement error. It happens because most elements exist as a mixture of isotopes — atoms with the same number of protons but different numbers of neutrons. Chlorine naturally occurs as about 75.8% chlorine-35 and 24.2% chlorine-37. The atomic mass is the weighted average of these isotopes, just like your grade point average reflects the weight of each course.
Atomic mass is measured in atomic mass units (amu), also called daltons (Da). One amu is defined as exactly 1/12 the mass of a carbon-12 atom. This unit is fantastically tiny — about 1.66 x 10⁻²⁴ grams — because atoms themselves are fantastically tiny. Using amu instead of grams makes the numbers manageable: a hydrogen atom is about 1.008 amu, an oxygen atom is about 15.999 amu, and a gold atom is about 196.97 amu.
It is crucial not to confuse atomic mass with atomic number. The atomic number counts only protons and defines the element, while atomic mass reflects the total mass of protons plus neutrons (electrons are so light they barely contribute). Two atoms of the same element always have the same atomic number but can have different atomic masses if they are different isotopes. This distinction matters in fields from nuclear medicine to archaeology, where scientists exploit isotope differences for everything from cancer treatment to dating ancient artifacts.