Difference Between Natural and Whole numbers

Introduction

Difference between natural and whole numbers is natural number is used to count objects ad whole numbers include 0 and natural numbers. Numerous other types of numbers exist, including whole numbers, natural numbers, integers, rational and irrational numbers, real and complex numbers, and integers. Students may find it puzzling more frequently than not, causing them to mix up one with the other.

Particularly in the natural numbers and whole numbers, since both of them resemble one another somewhat. Therefore, it is crucial that the students comprehend both whole numbers and natural numbers in detail.

In this tutorial, we will discuss the difference between natural numbers and whole numbers.

Natural Numbers

• Natural numbers are often referred to as counting numbers. As an illustration, the numbers we count on our hands are 1, 2, 3, 4, 5, and so forth.

• Natural numbers are, by definition, those that can be counted on our hands and only consist of positive integers starting at 1.

• The smallest natural number is generally thought to be 1, or just 1. As a result, fractions, decimals, and negative integers are not regarded as natural numbers. 46, 72, 25, 888, 560, etc. are a few examples of natural numbers.

Whole Numbers

• Whole numbers are ones that also contain positive integers besides 0. On a number line, these are shown on the right side.

• The smallest whole number is regarded to be 0, or zero. It should be noted that while fractions and decimals do not fall under the category of whole numbers, positive integers and natural numbers are.

• Whole numbers can be used in arithmetic operations such as addition, subtraction, multiplication, and division. Whole numbers include things like 0, 15, 37, 97, 67, etc.

Difference between Natural and Whole Number

Natural Number	Whole Number
All positive numbers from 1 to infinity are considered natural numbers and are therefore a part of the number system.	All natural numbers and 0 are included in the case of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions.
The natural number range is given by N = 1, 2, 3…..	W = 0, 1, 2, 3,... is the set of all whole numbers.
Natural number one is the smallest	The least whole number is zero.
With the exception of 0, every whole number is a natural number.	Every natural number is a whole number.

Algebra of Natural and Whole Numbers

• Addition − The outcome of the addition of two natural numbers or whole numbers is always a natural number or a whole number. Take any two natural numbers, such as 3 and 9, as an example. Now 3 + 9 = 12. 12 is a whole or natural number. As a result, the addition closes the system.

• Subtraction − A whole number or natural number is not always the outcome of subtracting two whole numbers or natural numbers. Take any two natural numbers, such as 3 and 9, as an example. 3 - 9 now equals -6, which is not a natural or whole number. As a result, in addition, the system is not closed.

• Multiplication − A whole or natural number is always produced when two whole or natural numbers are multiplied. For instance, the natural number is 27 when 3 × 9 = 27. The system closes under multiplication as a result.

• Division − When two whole or natural numbers are divided, whole or natural numbers are not always the outcome. For instance,$\mathrm{3÷9=\frac{1}{3}}$ As a result, division has not closed the system.

Solved Examples

1) Find the whole number among the following numbers 0, 7, 10, -21, -56, 90.

Answer: The whole numbers from the list are 0, 7, 10, and 90.

2) Every whole number is also a natural number. Is this a true statement? Explain your conclusion.

Answer: No, not all whole numbers are natural numbers. Natural numbers are by definition a subset of the number system, which includes all positive integers from 1 to infinity. As opposed to this, whole numbers are all positive numbers, from 0 to infinity.

Despite not being a natural number, 0 is a whole number. As a result, all whole integers other than 0 are present in natural numbers. As a result, it is untrue to say that every whole number is a natural number.

3) From the following list, pick out the whole numbers and natural numbers that are 4.5, 121, 4, -79, 0, and 30.

Answer: The difference between whole numbers and natural numbers is that whole numbers also include 0 and positive integers, but natural numbers only include positive integers from the list provided,

The whole numbers are 121, 4, 0, and 30 and the natural numbers are 121, 4, and 30.

4) Find whole numbers from 4, 0, (0.97), 2, -6, -17, and 21.

Answer: 4, 0, 2, and 21 are whole numbers.

5) Determine the natural numbers from the following series of integers. 41, (0.4), 5, 90, -91, 0, -7.

Answer: 41, 5, and 90 are natural numbers.

6) Determine the natural numbers from the following series of integers. 4, 1/2, 0, (0.87), 2, -7, -17, 21.

Answer: 4, 2, and 21 are Natural Numbers.

Conclusion

The numbers that are used for counting and are a subset of real numbers are known as natural numbers. Only positive integers are included in the set of natural numbers.

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.

The number 0 which is only a portion of the set of whole numbers and is absent from the set of natural numbers is the primary distinction between whole numbers and natural numbers.

FAQs

1. What are Whole Numbers in mathematics?

Positive integers and 0 are whole numbers in mathematics. It is a collection of natural numbers and 0, in other words. Whole numbers do not include fractions, negative integers, or decimals.

2. What is a natural number in mathematics?

Natural numbers are those that begin at one and go all the way to infinity. In other words, natural numbers do not include 0 or any other negative or fractional numbers and are strictly counting numbers. Some instances of natural numbers include 1, 6, 89, 345, and so forth.

3. How do natural numbers and whole numbers differ?

The main difference is the number zero, which does not belong to the natural number

4. What makes Natural Numbers "Natural"?

Because they are employed for counting organically, natural numbers are just that natural. Because it is logical or "natural," the set of natural numbers is the most fundamental number system.

5. Is the number zero a Natural Number?

The number zero is not a natural number. Natural numbers can be written out in the following order: 1, 2, 3, 4, 5, and so forth. But 0 belongs to the group of whole numbers and integers.