The numbers play a very important role in our day to day life. We use numbers to count, measure, compare and order things. We can order the things in increasing or decreasing fashion.
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Ascending order: Ordering of things from smallest to biggest. Ex: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and so on Descending order: Ordering of things from biggest to smallest. Ex: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 and so on |
The most widely and globally used system of numbers is Hindu-Arabic number system. Hindu number system was invented by Indian mathematicians between 1st and 4th centuries. Later, by 9th century, this system was adopted by Arabic mathematicians and finally, this came to be known as Hindu-Arabic number system. It future spread to Europe.
Hindu-Arabic numbers are the combination of just 10 digits or symbols: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. Out of these ten digits 0 is called as insignificant digit and all the remaining are called significant digits. This system is purely a place-value system where the digit zero has its own importance.
Representing a number: To write a number, the digits are placed from left to right under the places labelled as Units, Tens, Hundreds, Thousands… etc., and read accordingly.
For example, consider number 593071423. The following is the way in which it is represented or written and read.
This number can be represented or written as,
This number can be read as,Fifty nine crores thirty lakh seventy one thousand four hundred and twenty three.
The main difference between the Indian number system and International number system is the placement of the separators or comas. In international numbering system, millions are written after thousands while in Indian system, lakhs are written after thousands. Indian system is followed in India, Pakistan and Bangladesh. It is still called as Indian number system owing to it Union (Indian sub-continent) during the British rule.
Million and Billion are international units of number system. This system is based on ten to the power three (103). It has a three digit split in the numbers. This system is commonly used in western countries.
Whereas,
Lakh and Crores are Indian units of number system. This system starts with ten to the power three (103) and then is followed by two digit split after the hundredth place.
The following is the table showing the differences in the placement of separators in Indian as well as international number system:
A mathematical symbol which represents a number is called as numeral. The place of a digit is defined by its position. A digit in a particular number has two values namely, Face value and Place value.
Face value: The face value of a digit is the digit itself irrespective of its place. The value attributed to a digit by virtue of its face is called Face value.
Let us continue with the previous example,
| Ten crores | Crores | Ten Lakhs | Lakhs | Ten Thousands | Thousands | Hundreds | Tens | Units |
|---|---|---|---|---|---|---|---|---|
| 5 | 9 | 3 | 0 | 7 | 1 | 4 | 2 | 3 |
The face value of 5 is 5 itself; face value of 9 is 9 itself and so on.
Place value: The place value of a digit is the product of its place and its face value. The value attributed to a digit by virtue of its place is called Place value. Place value is also called local value of digit.
From the above example, the place value of 5 is fifty crores; place value of 9 is nine crores.
Another way to write it is,
500000000 = 5 x 108
90000000 = 9 x 107
3000000 = 3 x 106
000000 = 0
70000 = 7 x 104
1000 = 1 x 103
400 = 4 x 102
20 = 2 x 101
3 = 3 x 100
Numbers are usually read out using place values and not face values. To obtain the place value of a digit, we must multiply the digit with the value of its place in the given number. The representation of the place value as the product of the place of the digit and it face value is shown in the following table:
| Numeral | Face value | Multiply | Place | = | Place value |
|---|---|---|---|---|---|
| 3 | 3 | X | 1 | = | 3 |
| 2 | 2 | X | 10 | = | 20 |
| 4 | 4 | X | 100 | = | 400 |
| 1 | 1 | X | 1000 | = | 1000 |
| 7 | 7 | X | 10000 | = | 70000 |
| 0 | 0 | X | 100000 | = | 0 |
| 3 | 3 | X | 1000000 | = | 3000000 |
| 9 | 9 | X | 10000000 | = | 90000000 |
| 5 | 5 | X | 100000000 | = | 500000000 |
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