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To express extremely large numbers or extremely small numbers in an easier way. Sort of like saying cuz instead of because.
Scientific notation doesn't stop at a centillion. 1 centillion in scientific notation is 1 * 10303, but you can also write 1 * 10304 or even 9 * 109999999 in scientific notation. There is no upper limit to the numbers you can write in scientific notation.
Scientific notation is useful in economics to compute very large or very small numbers.
Scientific notation is required for very large or very small numbers.
Scientific notation is applied wherever numbers are very large or very small.