Advantage of Hindu Arabic numeration system

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the advantages of hindu-arabic numeral system are given below:

the first advantage is that there is place value in the hindu-arabic system

the second and the last advantage is that it has 0 which is very important part of the hindu-arabic numeral system

by saksham

Just to explain what a “place system” actually is look at the contrast between the two systems.

For the Romans “C” stood for “one hundred” wherever you find it. If you want more hundreds, you add an extra “C”. If you want a “one” (just a single unit) you use “I” – and “I” means “one unit”, (not one ten or one hundred) wherever you find it.

In the early days the Romans used to write “four” as four ones, “IIII”, but that was inconvenient, so they started saying “actually four is just one less than five”, they already had a symbol for “five” – “V”, so they wrote four as “IV” “one less than five” (since the one came before the five), and six as “VI” – or “one more than five” (since the one came after the five)

Suppose you want to write two hundred and thirty seven in the Roman system. First you need to work out the two hundred – that’s two lots of one hundred, which we write as “CC” (since “C” stands for a hundred), then we want thirty as three lots of ten, which is “XXX” (since “X” stands for ten) and then we need seven, which has to be written as five “V” plus two ones “I”. Total answer CCXXXVII.

Now let’s try writing five hundred and forty nine. Now five hundred has its own symbol “D” and when we are writing a nine, we treat that as “ten less one” and forty-nine is “fifty less one”. Fifty has its own symbol “L”, so forty nine is “IL” (one less than fifty) – so five hundred and forty-nine is “DIL”

So, to those used to the “Arabic” system (the one we use today):

237 = CCXXXVII

549 = DIL

You don’t tell how important a symbol is by where you find it. It means the same wherever you see it. The “I” means “one” – just a singe unit, whether it’s at the end of a number (like the two ones after five in the “seven” bit) or in the middle (like the “one less than fifty”) in “IL” – or “forty-nine”.

But Arabic is a “place” system. So what does that expression mean?

Look at the “Arabic” system. Pretend you’re a Roman used to the “absolute” value (I=”one” wherever you find it). Now let’s write one hundred and thirty-one in the Arabic system.

131 – now you have “one” turning up twice in that system, but the first time it means “one hundred” and the second time it means “one unit”. And the “3” in the middle means “thirty” – not “three” or “three hundred”. This is complicated to someone who’s used to the “absolute” system of the Roman numerals!

We teach children at school, that numbers work in columns

hundreds tens units

1 3 1

one hundred, plus 3 tens (thirty) and one unit – 131.

113 has the same actual digits in – two lots of one and a three, but means something different, because they are in different places

hundreds tens units

1 1 3

one hundred, plus one ten, plus 3 units = 113

And “311” means something else again.

So the value of a digit (a one, two, three, four etc) depends on where you place it – in the hundreds, tens or units columns. You can keep doing this for as long as you want – a column for thousands, for tens of thousand, hundreds of thousands and so on.

3,955,341 is a lot of digits, but we know that the second “3” is in the “hundreds” column and the first in the “millions” column. We usually write numbers with commas to help us tell at a glance which column something is in

3,955,341 is easy to read than “3955341” but it means the same thing.

It also makes arithmetic a lot easier. Look at the first two numbers written in Roman numerals:

237 = CCXXXVII

549 = DIL

You can’t add them up by “place value” – the first “C” is no bigger than the second one. In fact the whole second number is bigger than the first one – so the number of digits doesn’t tell you how big the number is. Go to the third column from the right and in the Roman numeral you have “V” in the first number and “D” in the second. But one is only five units while the other is five hundreds – so you can’t use a “column system” of adding up at all.

In the Arabic system, however, you have a “7” and a “9” in the first column and you can add them up because they are in the same place – the “7” is seven units and the “9” is nine units. When you come to the third column “2” is two hundred and “5” is five hundreds.

This answer is already long enough, without adding an explanation of what the Romans lacked, because they didn’t have a “0” – but it comes down to the place system again, in the end.