Why do you have exponetial notation?

Answer 1

Exponential notation is used to write really big numbers in smaller forms. Without this, extremely large numbers could not easily be used on a regular medium such as paper.

For example, the mass of the earth is about 5.98 x 1024 kilograms. Without scientific notation (which uses exponents of course), that number would require 25 characters to write out, instead of the nine characters used here.

Another reason that exponents are so useful is the fact that they allow us to group data together, making it simpler to work with. Take this equation for example:

a × a × 1/a × 3/a × 7a × 2a = 7

With all of those "a" terms being separate, there is no simple way to solve that equation. With exponents on the other hand, we can group those terms together and say:

∴ 42a4 / a2 = 7

∴ 42a2 = 7

∴ a2 = 7/42

∴ a = (1/6)1/2

∴ a = 61/2 / 6 ≈ 0.40825