Smallest Whole Number Explained: Definition and Examples

What are Whole Numbers?

Whole numbers include all natural numbers plus the number zero. This simple addition significantly expands the scope of numerical operations.

• Definition: The set of whole numbers starts with 0 and extends indefinitely (0, 1, 2, 3, …).

• Symbol: Represented by the symbol .

• Characteristics: Whole numbers do not include fractions, decimals, or negative numbers.

• Importance: They are integral to basic arithmetic operations and serve as a cornerstone for more complex number systems.

What is Smallest Whole Number?

The smallest whole number is 0 (zero), as whole numbers include all non-negative integers starting from zero and going up infinitely: {0, 1, 2, 3, ...}. Unlike natural numbers, which begin at 1, whole numbers add zero as the least element on the number line, neither positive nor negative. Zero acts as a placeholder with no value but essential place value, making it the foundation for counting and arithmetic.  

Identifying Smallest Whole Number

The question, "what is the smallest whole number?" has a straightforward answer. Given the definition that whole numbers commence with zero, zero is the initiating digit.

• Direct Answer: The number 0 (zero) is the smallest whole number.

• Reasoning: Since whole numbers are defined as the set {0, 1, 2, 3, …}, zero is the first element in this sequence. No whole number exists that is smaller than zero.

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Whole Number Properties

Several properties govern the behavior of whole numbers under various operations. These properties are fundamental.

1. Commutative Property

The commutative property means that the order of numbers does not affect the result in addition or multiplication.

Examples:

• Addition: 6 + 8 = 8 + 6 = 14

• Multiplication: 4 × 9 = 9 × 4 = 36

Formula:

• Addition: a + b = b + a

• Multiplication: a × b = b × a

2. Associative Property

The associative property states that the way numbers are grouped in addition or multiplication does not change the result.

Examples:

• Addition: (2 + 3) + 5 = 2 + (3 + 5) = 10

• Multiplication: (2 × 3) × 4 = 2 × (3 × 4) = 24
  
  

Formula:

• Addition: (a + b) + c = a + (b + c)

• Multiplication: (a × b) × c = a × (b × c)

3. Distributive Property

The distributive property connects multiplication and addition. It says:

• Multiplying a number by a sum of numbers equals the sum of multiplying the number individually.

Examples:

• 3 × (4 + 5) = (3 × 4) + (3 × 5) = 12 + 15 = 27

Formula:

1. a × (b + c) = (a × b) + (a × c)

Read More: Co Prime Numbers

Counting of Whole Numbers

While we can state the smallest whole number is zero, we cannot state the largest. The set of whole numbers is infinite. When we talk about counting, we typically mean enumerating elements within a finite subset or understanding the sequence itself. Whole numbers provide the framework for our fundamental counting operations, starting from zero. These properties and concepts are vital for building a strong mathematical foundation.

Whole Numbers Examples

Here are examples based on Whole numbers for you to practice and enhance your understanding of Whole Numbers: 

1. What is the smallest whole number?

Answer: 0

2. Write the first seven whole numbers.

Answer: 0, 1, 2, 3, 4, 5, 6

3. Is 15 a whole number?

Answer: Yes, 15 is a whole number because whole numbers include all numbers starting from 0.

4. Is -8 a whole number? Why?

Answer: No, -8 is not a whole number because whole numbers are never negative.

5. Find the successor of 49.

Answer: Successor of 49 = 49 + 1 = 50

6. Find the predecessor of 72.

Answer: Predecessor of 72 = 72 - 1 = 71

7. Which is greater: the smallest whole number or the smallest natural number?

Answer: The smallest whole number is 0 and the smallest natural number is 1.
So, 1 is greater.

8. Use the commutative property of addition to check: 12 + 25 = 25 + 12

Solution:
12 + 25 = 37
25 + 12 = 37
Since both results are equal, the commutative property holds.

9. Use the closure property to check whether 18 * 5 is a whole number.

Solution:
18 * 5 = 90
90 is a whole number, so the closure property holds.

10. Use distributive property to solve: 7 * (4 + 6)

Solution:
7 * (4 + 6) = (7 * 4) + (7 * 6)
= 28 + 42
= 70

Also Read: Rational Numbers

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