Numeral systems are ways of expressing numbers. Each system uses a certain set of signs and has its own rules.
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This is undoubtedly the most simple of all types of systems. To express a value n, we repeat one symbol (tally mark) n times. For example, to represent "5" using the symbol "/", we would write "/////". Why don't we use it in maths class? It's impractical - imagine writing 100 using this system or multiplying two numbers.
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In this system, a certain value corresponds to a certain sign, regardless of its location in the notation. The quantities are then added, subtracted (eg. Roman system) or multiplied, depending on the system.
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The value of a digit depends on its location within the number. The place where a certain digit is located represents the power of the base of the system. Most of the systems we use nowadays belong to this group.