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One of the major differences between natural numbers and whole numbers is the presence of value ‘0’ in whole numbers. A number can be defined as an arithmetic value which is used to represent a particular quantity.
- The natural number consists of all positive integers from 1 to ∞.
- On the other hand, a whole number consists of all integers from 0 to ∞.
- In Mathematics, the different types of numbers are classified based on their characteristic.
- Integers, Real Numbers, Natural Numbers, Rational Numbers, Whole numbers and Complex Numbers are some numbers.
- The decimal system is also part of the number system.
- Difference between natural numbers and whole numbers is related to the value zero.
- Numbers are used for counting, measurement and labelling.
Key Terms: Difference between natural numbers and whole numbers, Natural Numbers, Whole Numbers, Rational Numbers, Numbers, Number System, Integers, Decimal System, Real Numbers, Rational Numbers
What are Whole Numbers?
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Before knowing the difference between whole numbers and natural numbers, it is very important students first understand whole numbers and natural numbers as separate entities.
- The whole number belongs to a number system that includes positive integers, including 0.
- The smallest number is zero.
- These numbers are present on the right side of the number line.
- Natural numbers also belong to the category of these numbers.
- This means all natural numbers belong to the category of whole numbers, but not all whole numbers are natural numbers.
- Fractions, decimal values, complex numbers, and so on are not whole numbers.
Whole Numbers: 0, 1, 2, 3,……….., ∞
Example of What are Whole Numbers?Example 1: 112 is a positive integer and a whole number. Example 2: -17 is a negative integer and not a whole number. Example 3: 352 is a whole number and a positive integer. Example 4: 4.5 is a decimal value thus it is not a whole number. |
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What are Natural Numbers?
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Natural numbers are just like whole numbers. You need to remove 0 from whole numbers, and you will get natural numbers. All positive integers other than 0 are natural numbers.
- 0 and negative integers are not natural numbers.
- The smallest natural number is 1.
- These numbers are also known as counting numbers, as they can be counted on hands.
- They are represented on the right side of the number line.
- It consists of only positive integers from 1 to ∞.
Example of What are Natural Numbers?Example 1: 17 is a positive integer and a natural number. Example 2: -34 is not a negative integer and is not a whole number. Example 3: 99 is a natural number and a positive integer. Example 4: 10/7 is not a natural number as it is a fraction. |
Difference between Natural Numbers and Whole Numbers
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The most important and the key difference between natural numbers and whole numbers is the number 0. The various differences between natural numbers and whole numbers are mentioned below.
| Natural Numbers | Whole Numbers |
|---|---|
| Natural numbers are the counting numbers that start with 1. | Whole numbers are the natural numbers along with zero. It starts with 0. |
| The smallest whole number is zero. | The smallest whole number is one. |
| All natural numbers are considered whole numbers. | All whole numbers are not considered natural numbers. |
| They are depicted by the letter ‘N’ | They are depicted by the letter ‘W’ |
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Things to Remember
- Numbers are used to represent arithmetic quantity.
- Natural numbers and whole numbers are represented by the letters ‘N’ and ‘W’, respectively.
- Zero is the smallest whole number, and one is the smallest natural number.
- The main difference between natural number and whole number is related to the number zero.
- Prime Numbers, Co-prime numbers, Even and Odd numbers and Perfect numbers are types of natural numbers.
Sample Questions
Ques. Identify natural numbers from the given list: 0, 75, -43, 3.14 and 99. (1 mark)
Ans. From the given list natural numbers are 75 and 99.
Ques. Is -47 a natural number? (1 mark)
Ans. No, -47 is not a natural number because it is a negative integer. Only positive integers are natural numbers.
Ques. Find out the whole numbers from the following: 17, 25, 49.8 and 0. (1 mark)
Ans. From the given list whole numbers are 17, 25 and 0.
Ques. What is the key difference between natural numbers and whole numbers? (1 mark)
Ans. The key difference between natural numbers and whole numbers is 0. Zero is a whole number but not a natural number.
Ques. Are all natural numbers considered as whole numbers? (1 mark)
Ans. Yes, all natural numbers are considered whole numbers. One thing must be kept in mind, that one cannot consider all whole numbers as natural numbers since they contain 0 as well.
Ques. Which alphabet is used to represent natural numbers? (1 mark)
Ans. In mathematics, the alphabet ‘N’ is used to represent natural numbers.
Ques. Which is the smallest whole number? (1 mark)
Ans. The smallest whole number is 0.
Ques. Find out the whole numbers and natural numbers from the given list: 27, 56, 0, 2.67, -67, ¾, 10 and 23. (1 mark)
Ans. The whole numbers from the above given list are 27, 56, 0 and 23.
Natural numbers from the above given list are 27, 56 and 23.
Ques. Are whole numbers and natural numbers same? (1 mark)
Ans. Whole numbers are comprised of all the natural numbers along with zero. It starts from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on. However, all whole numbers are not natural numbers.
Ques. Find three consecutive whole numbers whose sum is more than 36 but less than 45. (2 marks)
Ans. Let the numbers be (n-1), n, and (n+1)
Sum of three numbers = 3n
hence 36 < 3n < 45 or 12 < n < 15
hence numbers 13, 14, and 15
Ques. Find three consecutive numbers such that the sum of twice the greatest number and thrice the least number is 54. (2 marks)
Ans. Let the numbers be (n-1), n, and (n+1).
2(n+1)+3(n-1) = 54
5n -1 = 54 or 5n = 55 or n = 11
hence numbers are 10, 11 and 12
Ques. Identify whole numbers from the given numbers: 7/9, 0, 9, 69.6, 20, -21, -56, 80. (2 marks)
Ans. From the given list, the whole numbers are 0, 9, 20, and 80
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