What are the advantages of HIndu Arabic system of numeration?

Answer 1

Because it has a zero symbol the advantages are that addition, subtraction, division and multiplication operations are easier to be carried out than a numeration system that does not have a zero symbol like the Roman numeral system.

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The other advantage of the Arabic system - even more important than the zero (which can be, and has been, added into the Roman system) is that the Arabic system is a "place system". This means that the value of a digit depends on where it occurs in a number.

This means that 113, 131 and 311 all mean something different, although they have exactly the same digits in them and exactly the same number of digits. This is because the 3 in the first number (113) means 3 "units" (just plain "three"). It means 3 tens (or "thirty") in the second number (131) and three hundreds (which we pronounce "three hundred") in the number 311.

A place system can be seen as putting things into columns. You work from right to left, putting the number of units in the first column, the number of tens in the next and so on through hundreds, thousands, tens of thousands and so on.

In fact there is no limit to number of digits you can add. Though after a while there are so many digits that, even with commas to help, there are too many to be readable, and people who habitually use very large numbers (like astronomers and physicists) adopt one of a number of modifications to the standard Arabic system. We have also recently (20th century) had to add extra names to the Arabic system - like "trillion" to cope with numbers like national debts!

However, the place system with only the numbers we use to count with ("One, two, three, four" and so on) has a major weakness. Using those numbers means that you have no way of showing that you have nothing in a particular place - so if you have the number "three hundred and one" and you are using the Arabic system without a zero you would have to leave a blank and write three hundred and one as 3 1 - to show that you have 3 hundreds and 1 unit, but no tens. Now 3 1 is easy to mistake for thirty-one or even for three thousand and one.

So, to show that any particular column is blank, we now have the zero sign, so "three hundred and one" is written 301, and is easy to distinguish from "thirty-one" (31) and three thousand and one (3001). This is why the zero is so important - it makes the column system really efficient.

Once you have this system you can use a column system for all sorts of arithmetical calculations, which can be done on paper, or written on sand tables or, of course, on computers.

The so-called Arabic numbering system (really derived from Indian mathematicians) arrived in Europe in what we now call the late Middle Ages. It made possible more complex operations involving multiplication and division which were previously the territory only of the skilled abacus user. It revolutionised not only scientific calculation, but also commercial and financial calculation and made possible the development of modern book-keeping systems.