Final answer:
We can demonstrate that whole numbers are not closed under division by using 3 and 2, as their quotient is 1.5, a decimal, and not a whole number. This example proves that division can yield results outside of the original set.
Step-by-step explanation:
To show that the set of whole numbers is not closed under division, we can find two whole numbers whose quotient is not a whole number. For instance, let's take the whole numbers 3 and 2. If we divide 3 by 2, the quotient is 1.5, which is not a whole number but a decimal. This example demonstrates that when we perform the division of some whole numbers, the result is not necessarily within the set of whole numbers.
Additionally, when discussing division in terms of significant figures, the product or quotient should match up to the least number of significant figures from the factors used in the operation as per Example B9 rules.
The set of whole numbers is not closed under division because there are cases where the quotient is not a whole number. To show this, we can take the example of dividing 4 by 3. When we divide 4 by 3, we get a quotient of 1.333... which is not a whole number.
The division of 4 by 3 results in a recurring decimal, indicating that the quotient is not a whole number. This demonstrates that the set of whole numbers is not closed under division.