I have been asked to provide at least two real-world numerical examples of scientific notation and discuss where and why it is necessary to use. Can anybody help me understand what this is asking me to do?
I am not sure about real world, but astrophysics uses scientific notation. When we refer to how far away a planet or star is, the number is so large that we need scientific notation to shorten it.
Scientific notation is useful because it allows us to concisely express very large or small numbers. It works by multiplying a number by a power of ten. For example, we could write 1,000,000,000,000 in scientific notation as 1 * 10^12 (equivalently, 1e12, 1E12). You can think of this as just adding the number of zeros in ten's exponent onto the number.
This question is asking you to give some real world examples of where this is used. One example is the speed of light. The speed of light is 299,792,458 meters/second, but it is often reported as 3e8 meters/second, as this is easier to recognize and do calculations with.
Another useful place is your calculator. If a result is really really big or small, it may not have enough room to fit on your calculator's screen, so scientific notation will be used.
There are many more uses, but I hope this serves as a good starting point for you, and I encourage you to think of some uses and find some more examples of your own.
8 words: it's just another way of writing big numbers