**Development of Numbers**

The history of human beings
has started from the hunting age called the primitive age. At that time the people were
in a primitive society. They were calculating anything by using concrete or
stone. Later they started to draw lines and counted the cattle. Gradually the
sense had been developed in the human mind and they had started fingers as counting
tools.

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And during the time Hindu
Arabic digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 were developed. But 1, 2, 3, 4, 5,
6, 7, 8, 9 were useful in counting. Later they needed 0 to form different
numbers like 10, 20, 30, 40 and so on. In this way, 0 was included with natural
numbers to form whole numbers.

Zero is just nothing when we
write it single. But it is more thing when we write 0 just after 1, 2, 3, 4
etc. For number: 01, 02, 03, 04 are just 1, 2, 3 and 4 only. But 10, 20, 30, 40
are greater than 1, 2, 3, and 4 due to placement of zero from left to right.

**Numerals**

The symbols which indicate
numbers are called **numerals**. There are different numerals for different system
of numbers in the world. Some of the common systems and their numerals are as
given below in the table.

**Natural Numbers**

The numbers
which are based for counting are called **natural numbers**. For example: 1, 2, 3,
4, ……… ∞ (Infinite). It is also called
counting numbers. The set of natural numbers is denoted by N.

i.e. N = {1, 2, 3, 4, 5, 6, ………… }

**Whole Numbers**

When we
include 0 with the set of natural numbers then the new set of numbers is called the **whole number**. For example: 0, 1, 2, 3, 4, ……… ∞ (Infinite). The set of whole
numbers is denoted by W.

i.e. W = {0, 1, 2, 3, 4, 5, ………… }

**Greatest and Smallest Numbers**

The greatest and smallest
number of a single digit are 9 and 1 respectively. 0 itself is not considered
as a number. When it comes after any number, then it gives the value. For
example: 10, 20, 30, 100 etc. 01 is same as 1. So, we can form the greatest and
smallest number of certain number of digits as given below in the table:

We can form the greatest and smallest number of certain digits, for example say 0, 1, 2, 3, 4 and 5 as follows:

Greatest number: 543210

Smallest number:102345

**Worked
Out Examples**

*Example 1:**
Find the sum of the smallest 3 digit and greatest 3 digit number.*

*Solution:** *

*Here,*

*The greatest 3 digit number = 999*

*The smallest 3 digit number = 100*

*∴** The sum = 999 + 100 = 1099*

* *

*Example 2:**
Find the difference between greatest 4-digit number and smallest 3-digit
number.*

*Solution:** *

*Here,*

*The greatest 4 digit number = 9999*

*The smallest 3 digit number = 100*

*∴** The difference = 9999 – 100 =
9899*

* *

*Example 3:**
Find the sum of 9 ^{th} whole number and 100^{th} natural
number.*

*Solution:** *

*Here,*

*9 ^{th} whole number = 8*

*100 ^{th} natural number = 100*

*∴** The sum = 8 + 100 = 108*

* *

*Example 4:**
Use the digits 0, 1, 5, 7, 9 to form smallest and greatest number.*

*Solution:** *

*Here,*

*Smallest number = 10579*

*Greatest number = 97510*

* *

*Example 5:**
Find the value of the sum of roman numerals MMD and MCC.*

*Solution:** *

*Here,*

*MMD = 2500*

*MCC = 2200*

*∴** MMD + MCC = 2500 + 2200 = 3700** *

* *

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