Problem 456 - Prealgebra

Question

Determine which of the following are (a) counting numbers (b) whole numbers. $$0,1,75$$

Step-by-Step Solution

Answer

Counting numbers: 1, 75. Whole numbers: 0, 1, 75.

Step 1: Understand Counting Numbers

Counting numbers are the positive integers starting from 1 onward. They are used for counting objects. So, the series of counting numbers is 1, 2, 3, 4, and so on.

Step 2: Understand Whole Numbers

Whole numbers are all the non-negative integers, which include 0 and the counting numbers. So, the series of whole numbers is 0, 1, 2, 3, 4, and so on.

Step 3: Identify Counting Numbers in the Given Set

Check each number in the given set to see if it is a counting number. The set is [0,1,75], so we check:- 0 is not a counting number because counting numbers start from 1.- 1 is a counting number.- 75 is a counting number.Thus, the counting numbers in the set are 1 and 75.

Step 4: Identify Whole Numbers in the Given Set

Check each number in the given set to see if it is a whole number. The set is [0,1,75], so we check:- 0 is a whole number.- 1 is a whole number.- 75 is a whole number.Thus, the whole numbers in the set are 0, 1, and 75.

Key Concepts

Counting Numbers

Counting numbers are an essential part of mathematics. They start from 1 and go on infinitely. You use counting numbers when you count objects or items. For example, if you have three apples, you count them as 1, 2, and 3. Counting numbers are always positive and do not include zero.

In the context of the given set \[0, 1, 75\], counting numbers would be:

• 1: Yes, it starts the counting series.
• 75: Yes, it’s a positive integer.
• 0: No, it's not included since counting numbers start at 1.

So, the counting numbers here are 1 and 75.

Whole Numbers

Whole numbers broaden the scope a bit more than counting numbers. They include all counting numbers plus zero. Thus, the sequence starts from 0 and includes all the positive integers: 0, 1, 2, 3, and so on. This set is useful for representing a situation where having 'none' of something needs to be accounted for. For instance, if you have no apples, you count it as 0.

In the given set \[0, 1, 75\], the whole numbers would be:

• 0: Yes, since zero is the starting point of whole numbers.
• 1: Yes, it continues the sequence.
• 75: Yes, it's a positive integer.

Thus, all the numbers in the set 0, 1, and 75 are whole numbers.

Identifying Number Sets

When working with different types of numbers, recognizing the set they belong to is crucial. In many math problems, you'll need to categorize numbers as either counting numbers or whole numbers.

To identify the set a number belongs to, ask:

• Is it greater than or equal to 1? If yes, it's a counting number.
• Is it greater than or equal to 0? If yes, it's a whole number.

For example, given the set \[0, 1, 75\]:

• 0: Whole number (not a counting number)
• 1: Both a counting number and a whole number
• 75: Both a counting number and a whole number

This clarity helps solve mathematical problems accurately and efficiently, ensuring that you properly classify each number.