Numerals | Natural Numbers | Whole Numbers

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

 

Do you have any question regarding the above topic?

 

You can post your questions or problems in the comment section below.