Final answer:
Chronometric dating is the method that determines the numerical age of a fossil, often using radiocarbon dating, while relative dating places fossils in a sequence without providing their numerical age.
Step-by-step explanation:
The method that determines the age of a fossil on some specified time scale is b) chronometric, also known as absolute dating. This method measures the decay of radioactive elements within the fossils, such as carbon-14, to give an approximate numerical age in years. On the other hand, relative dating is a technique used to determine which fossils are older or younger compared to others, but it does not provide an exact age in years. Relative dating includes methods like stratigraphy, which relies on the ordering of rock layers to determine the sequence of historic life forms. In certain contexts, relative dating can be enhanced by typological sequencing, such as seriation, to place artifacts in chronological order based on cultural characteristics.