scientific notation is useful because when you are writing out a very large or very small number you dont have to write lots of zero'z
Because sometimes numbers get really big or really small.
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It is useful for expressing very small or very large numbers. For example, the SI unit for length is a metre. The distance to the sun is approx 149600000000 metres. Even in terms of kilometres, it is 149600000 km. It is easy to mistype or misread the number if zeros in such a number. It is much safer to represent the value as 1.496*10^11 metres.
Scientific notation becomes even more useful when considering even more extreme values such as the volume of a red blood cell is approx 8 * 10^-14 litres.
You have it in reverse. Scientific notation is useful for measuring stars.
Scientific notation is useful in economics to compute very large or very small numbers.
Scientific notation is useful in mathematics because it makes very large or very small numbers easier to compute.
You use scientific notation when it comes to "too large" or "too small" numbers. The reasons why using scientific notation is useful are that it saves time to do the computation and also that it makes people's life easier to compute values instead of writing them out completely!
Scientific notation gives a compact notation, which is especially useful for writing down - and doing calculations with - very large, and very small, numbers.