Session 1: What are Whole Numbers? – Definition, Symbol, Comparison and Examples

When did humans first use numbers?

In approximately between c. 5500 and 4000 BC, the Sumerians used natural numbers 1, 2, 3, …  The earliest counting did not progress very far because numbers were associated with items that were counted on fingers and toes. As civilizations grew and became more complex, the need also grew for a number system that could handle tasks requiring counting and performing operations with numbers.

Numbers are necessary to make all kinds of discoveries and developments. Whether we want to calculate how far the newly discovered star may be or describe the dimensions of a new strain of virus, we need to represent it in various ways. In this lesson, we will learn whole numbers and related concepts.

What are Natural Numbers?

Natural numbers are the numbers we use for counting or enumerating items. The set of natural numbers is denoted by N. Thus N =  {1,2,3,4… }. The set of natural numbers is infinite.

What are Whole Numbers?

Whole numbers are the set of natural numbers plus zero. The set of whole numbers is denoted by W. Thus W = {0,1,2,3,4,…. }

Representation of Whole Numbers on a Number Line

To represent whole numbers on a number line, we draw a line and choose an arbitrary point as 0. All the numbers on the right-hand side of 0 represent the natural numbers, whereas all the numbers along with 0 represent the whole numbers. Any whole number corresponds to a unique position on the number line.

The length between two consecutive whole numbers is called a unit length.

Comparing Whole Numbers

We can use the number line to compare and order whole numbers. Going from left to right, numbers increase in value. Going from right to left, numbers decrease in value. 

We can use inequality symbols to show the ordering of whole numbers. Remember to use the notation a<b (Read: a is less than b ) when a is to the left of b on the number line. We write a>b  (Read: a is greater than b ) when a is to the right of b on the number line.

From the number line, we observe that:

• There is no whole number on the left-hand side of 0. Thus, 0 is the smallest whole number.
• Each whole number has one and only one successor. The successor of a whole number is the number just on its right on the number line. Thus, 1 is the successor of 0, 2 is the successor of 1 and so on.
  0 is not the successor of any whole number.
• A whole number is greater than all the whole numbers that lie on its left on the number line.
  2 is to the left of 6 on the number line, so 2<6. 
•  A whole number is less than all the whole numbers that lie on its right on the number line.
  6 is to the right of 2 on the number line, so 2<6. 
• There is no whole number between two consecutive whole numbers, and there is at least one whole number between two non-consecutive whole numbers.
  Thus, there is no whole number between two consecutive whole numbers 2 and 3,  whereas the whole number 3 lies between two non-consecutive whole numbers 2 and 4. 

When the given whole numbers are small, we can easily represent them on a number line and compare them by observing the relative positions. However, if the given numbers are large, it is impractical first to represent them on a number line and then compare.

Steps to Compare Large Numbers

To compare large numbers, we adopt the following method:

Step 1:  If the number of digits in the given numbers is unequal, then the number having more digits is greater.

Step 2: If the number of digits in the given numbers is equal, then compare the digits at the highest place, the number having a greater digit ( at the highest place ) is greater. If the digits at the highest place are equal, then compare the digits at the next highest place, the number having a greater digit ( at the next highest place ) will be greater, and so on.

1) Compare 53456 and 54999. 

The number of digits in 53456 = 5  
The number of digits in 54999 = 5 
∴ Both the numbers have an equal number of digits.
In both 53456 and 54999, the digit in the ten thousand places is 5. Because they have the same number in the ten thousand place, we compare the digits in the thousands place.

When we look at both 53456 and 54999, in the thousands place, there is a 4 and a 3. The number with the 4 in the thousands place is larger.

Thus, 54999>53456.

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What are Whole Numbers? – Examples

Example 1

Write the successor of each of the following numbers:

i. 6548

ii. 7499

Since the successor is 1 more than the given number,

i. The successor of 6548=6548+1=6549

ii. The successor of 7499=7499+1=7500

Example 2

Write the predecessor of each of the following numbers:

i. 1352

ii. 9900

Since the predecessor is 1 less than the given number,

The predecessor of 1352=1352−1=1351

The predecessor of 9900=9900−1=9899

Example 3

Write the whole number whose successor is 743300.

The required whole number = predecessor of 743300

=743300−1
=743299

Example 4

Write the whole number whose predecessor is 329999.

The required whole number = successor of 329999

=329999+1
=330000

Example 5

Compare 75302 and 74392.

The number of digits in 75302 = 5 
The number of digits in 74392 = 5 
Both the numbers have equal digits.

In both the numbers the digit in the highest (ten thousands) place is 7. Because they have the same number in the ten thousand place, we compare the digits in the thousands place.

The digit in the thousands place in 75302 = 5 
The digit in the thousands place in 74392 = 4 
As 5>4,  therefore, 75302>74392.