Problem 3 - Prealgebra

Question

In the following exercises, determine which of the following numbers are a counting numbers b whole numbers. $$0, \frac{4}{9}, 3.9,50,221$$

Step-by-Step Solution

Answer

Counting Numbers: 50, 221. Whole Numbers: 0, 50, 221.

Step 1: Identify Counting Numbers

Counting numbers are the positive integers starting from 1, 2, 3, and so on. Examine each number in the given list to determine if it fits this description. The counting numbers from the list are 50 and 221.

Step 2: Identify Whole Numbers

Whole numbers include all the counting numbers along with 0. Check the list again to see which numbers fit this expanded category. The whole numbers from the list are 0, 50, and 221.

Key Concepts

counting numbers

Counting numbers are the basic numbers we start learning as children. They begin at 1 and include all positive integers without any fractions or decimals.
Examples of counting numbers are:

• 1
• 2
• 3
• 50
• 221

Counting numbers do not include 0, negative numbers, decimals or fractions.
In the given exercise, the numbers 50 and 221 belong to the group of counting numbers because:

• They are positive.
• They do not include any fractions or decimals.
• They start from 1 onwards.

whole numbers

Whole numbers are a step beyond counting numbers. They include all counting numbers and zero. Whole numbers do not include fractions, decimals, or negative numbers.
Examples of whole numbers are:

• 0
• 1
• 2
• 50
• 221

In the given exercise, the numbers 0, 50, and 221 belong to the group of whole numbers because:

• They are non-negative.
• They do not include any fractions or decimals.

positive integers

Positive integers are numbers greater than zero and do not include any fractions or decimals. They are very similar to counting numbers, but often the term 'positive integers' is used in more formal mathematical texts.
Examples of positive integers are:

• 1
• 2
• 3
• 50
• 221

In different contexts, you might see 'positive integers' being used interchangeably with 'counting numbers'.
In this exercise, the numbers 50 and 221 belong to the group of positive integers because:

• They are greater than zero.
• They do not include fractions or decimals.