How To Represent 0.1 In Floating Point Arithmetic And Decimal

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I am trying to understand floating point arithmetic better and have seen a few links to 'What Every Computer Scientist Should Know About Floating Point Arithmetic'.

I still don't understand how a number like 0.1 or 0.5 is stored in floats and as decimals.

Can someone please explain how it is laid out is memory?

I know about the float being two parts (i.e., a number to the power of something).

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