Linear Algebra and scaling method

Why we are not using all numbers in floating point arithmetic and interested in scaling for linear algebra?

If scaling is good so why floating point arithmetic contain large numbers?

As I know for large numbers the distance between two numbers are larger than distance between two small numbers. Is this a benefit for small numbers?

If you’re seeking help about Octave, please post your code and explain what problem you have with its scaling behavior. Also move this to Help in that case.

If it’s a general question about floating point, there are better guides elsewhere such as https://floating-point-gui.de/ and What Every Computer Scientist Should Know About Floating-Point Arithmetic

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