What are examples of scientific notation used in real life?
Elemental (atomic) quantities and cosmic (space) quantities, as well as many technological metrics.
As the name implies, its primary use is in the sciences, where huge ranges of values may be encountered. It is also often used when accuracy must be communicated consistently.
Chemists, physicists, astronomers and biologists (and related disciplines) use scientific notation on a regular basis.
"Common" usage is something else, as most daily interactions and metrics of life do not need the range or accuracy of scientific notation. But, if you do not at least understand how they are created and why they are used, you may miss some important information when they are used by other people.