After that comes a more difficult process: Finding a fossil merely places one organism within a time span. Finding many organisms places the group within a time span. Determining the actual existence-span of the species is very approximate. If the fossils are relatively rare, the actual existence-span may be much greater that the fossil record indicates. Even if the fossils are relatively abundant during the species' heyday, the number of organisms may have been small during the time of its appearance on Earth and during its demise.
At these important times, its fossil record might be sparse or nil, causing those times to be under-represented. The oldest method is stratigraphy, studying how deeply a fossil is buried.
Dinosaur fossils are usually found in sedimentary rock. Sedimentary rock layers strata are formed episodically as earth is deposited horizontally over time. Newer layers are formed on top of older layers, pressurizing them into rocks. Paleontologists can estimate the amount of time that has passed since the stratum containing the fossil was formed. Generally, deeper rocks and fossils are older than those found above them. Observations of the fluctuations of the Earth's magnetic field, which leaves different magnetic fields in rocks from different geological eras.
Dating a fossil in terms of approximately how many years old it is can be possible using radioisotope-dating of igneous rocks found near the fossil.
Unstable radioactive isotopes of elements, such as Uranium, decay at constant, known rates over time its half-life, which is over million years. An accurate estimate of the rock's age can be determined by examining the ratios of the remaining radioactive element and its daughters. For example, when lava cools, it has no lead content but it does contain some radioactive Uranium U Over time, the unstable radioactive Uranium decays into its daughter, Lead, at a constant, known rate its half-life.
By comparing the relative proportion of Uranium and Lead, the age of the igneous rock can be determined. Potassium which decays to argon is also used to date fossils.
The half-life of carbon is 5, years. That means that half of the C decays into nitrogen in 5, years. Half of the remaining C decays in the next 5, years, etc. This is too short a half-life to date dinosaurs; C dating is useful for dating items up to about 50, - 60, years ago useful for dating organiams like Neanderthal man and ice age animals. Radioisotope dating cannot be used directly on fossils since they don't contain the unstable radioactive isotopes used in the dating process.
To determine a fossil's age, igneous layers volcanic rock beneath the fossil predating the fossil and above it representing a time after the dinosaur's existence are dated, resulting in a time-range for the dinosaur's life. Thus, dinosaurs are dated with respect to volcanic eruptions.
Looking for index fossils - Certain common fossils are important in determining ancient biological history. These fossil are widely distributed around the Earth but limited in time span. Examples of index fossils include brachiopods which appeared in the Cambrian period , trilobites which probably originated in the pre-Cambrian or early Paleozoic and are common throughout the Paleozoic layer - about half of Paleozoic fossils are trilobites , ammonites from the Triassic and Jurassic periods, and went extinct during the K-T extinction , many nanofossils microscopic fossils from various eras which are widely distributed, abundant, and time-specific , etc.