Natural Numbers and Whole Numbers

Example 1:

Determine the whole numbers from the given list of numbers: \(\mathbf{\frac{5}{7}}\), 0, 3, 46.5, 50, – 31, – 96, 170.

Solution: 

The list of numbers we have are \(\frac{5}{7}\), 0, 3, 46.5, 50, – 31, – 96, 170

As we know that fractions, decimals, and negative numbers are not considered as whole numbers, then, in this case the whole numbers we can observe in the list are 0, 3, 50, and 170.

Example 2:

For a particular question in the competition, Adam said, “Every whole number is a natural number!” while Jenny responded, “All natural numbers are whole numbers!” 

Find the competitor who gave the correct answer.

Solution:

As stated, Adam said that every whole number is a natural number. But Jenny countered it by saying that all natural numbers are whole numbers. According to the definition of the number system, natural numbers are a set of positive integers starting from 1, but whole numbers start from 0. From this, we can conclude that all the natural numbers are whole numbers, but not all the whole numbers are natural numbers.

Hence, Jenny stated the correct answer.

Example 3: 

Find out the whole numbers and natural numbers from the given series 2.5, 123, \(\mathbf{\frac{7}{80}}\), 10, – 9, 0, 28, 152, and 1.

Solution: 

The given series of numbers are 2.5, 123, \(\frac{7}{80}\), 10, – 9, 0, 28, 152, 1.

From the given list we can separate the whole numbers and natural numbers into two lists:

Whole numbers are 123, 10, 0, 28, 152, and 1.

Natural numbers are 123, 10, 28, 152, and 1.