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Hindu Arabic numeration?

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August 17, 2008 2:31AM

HINDU-ARABIC NUMERATION

Over the years people invented systems to communicate number ideas. Each number system or numeration is made up of symbols and the rules for combining these symbols. There are different number systems that are known but the Hindu-Arabic numeration is what most countries use today.

The Hindu-Arabic numeration originated with the Hindus in India and then developed by the Arabs who introduced it to Western Europe. Eventually, the system spread to other parts of the world.

Numbers are ideas and, like any other idea, we have symbols to represent them. The symbols that are used to represent numbers called numerals.

So when we say write a number, we actually mean write a numeral for the number.

Examples of symbols to represent the number five:

lllll 5 v

There are ten different standard symbols called digits to write numbers.

0 1 2 3 4 5 6 7 8 9

Just as we put together letters to form words to communicate our thoughts, we put together digits to communicate numbers. We can therefore think of digits as the

"alphabet" of our number systems.

To form a number we combine digits. However, even if the digits in one number are the same in another, it does not mean that the numbers are the same.

Same digits but different numbers

658 685 586 568 856 856

The Hindu-Arabic numeration is based on 10. That means the system is based on grouping by powers of ten.

10 1 = 10 10 10 = 100 10 100 = 1000 and so on.

Hence, the order of the place value in our number system is as follows:

millions hundred thousands ten thousands thousands hundreds tens ones

10 10 10 10 10 10 1

x x x x x x

100,000 10,000 1,000 100 10 1

= = = = = =

1 000 000 100 000 10,000 1,000 100 10

Each place value is 10 times greater than the place value next right to it or 10 times less than the place value next left to it. Thus, hundreds is 10 times greater than tens place or 10 times less than the thousands place.

Let us compare the numerals 658 and 568.

6 in 658 is 6 x 100 = 600, because 6 is in the hundreds place

6 in 568 is 6 x 10 = 60, because 6 is in the tens place

The value of 6 in 658 is different from 6 in 568, so 658 and 568 are the two different numbers even if they have the same digits.

Look at the place value chart again.

Notice that as the place value becomes greater, the number of zeroes becomes more, because we multiply each place 10 times next right to it. There are 6 places from millions to ones place, so the value of trillions place is:

10 x 10 x 10 x 10 x 10 x 10 or 10 to the power of 106

106 (read as ten to the sixth power) is an example of exponential notation.

An exponential notation is another way of expressing a number that is repeatedly multiplied by itself. 10 is multiplied by 6 times, hence 106.

The small number 6 in 106 is called exponent and the 10 is the base. The exponent tells how many times the base is taken as a factor. The exponent in 106 also indicate how many zeroes there are in the number after 1. We can see that one million has 6 zeroes.

Study the equivalent exponential notations for each place value.

Millions 10 x 10 x 10 x 10 x 10 x 10 =106

Hundred Thousands 10 x 10 x 10 x 10 x 10 =105

Ten Thousands 10 x 10 x 10 x 10 =104

Thousands 10 x 10 x 10 =103

Hundreds 10 x 10 =102

Tens 10=101

Ones 1 =100

The value of a digit depends on its place value positio in a number. For example, the value of 8 in 85 692 is 80 000, because it is in the ten thousands (104) place.

8 x (104) = 80 000

If we expand the number 85 692 using exponential notation we will also get the value of each digit.

85 692 = (8 x 104) + (5 x 103) + (6 x 102) + (9 x 101) + (2 x 100)

= 80 000 + 5 000 + 600 + 90 + 2

= 85 692

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