Problem 579 - Prealgebra

Question

Determine which of the following numbers are (a) counting numbers (b) whole numbers. 0, 4, 87

Step-by-Step Solution

Answer

(a) Counting numbers: 4, 87. (b) Whole numbers: 0, 4, 87.

Step 1 - Identify Counting Numbers

Counting numbers are the set of positive integers starting from 1. So, identify the numbers that are greater than zero and are positive integers.

Step 2 - List Counting Numbers

The given numbers are 0, 4, and 87. Out of these, 4 and 87 are positive integers. So, the counting numbers are 4 and 87.

Step 3 - Identify Whole Numbers

Whole numbers include all non-negative integers. So, identify the numbers that are greater than or equal to zero.

Step 4 - List Whole Numbers

The given numbers are 0, 4, and 87. All these numbers are non-negative integers. So, the whole numbers are 0, 4, and 87.

Key Concepts

Counting Numbers

Counting numbers are the numbers we typically use when we count objects. These numbers are sometimes referred to as natural numbers, but they strictly start from the number 1 and move upwards.

To put it another way:

• Counting numbers: 1, 2, 3, 4, 5, 6, 7, ... and so on.

They do not include zero, negative numbers, fractions, or decimals.

In the given list (0, 4, and 87), the counting numbers are 4 and 87 because they both are positive integers starting from 1.

Whole Numbers

Whole numbers are a bit more inclusive than counting numbers. They contain all counting numbers and add the number zero. They start from zero and extend infinitely to the right.

In simpler terms:

• Whole numbers: 0, 1, 2, 3, 4, 5, 6, 7, ... and so on.

This means whole numbers do not include negative numbers, fractions, or decimals.

From our list (0, 4, and 87), all numbers are classified as whole numbers because they are all non-negative integers.

Positive Integers

Positive integers are all the integers that are greater than zero. In other words, they do not include zero or any negative numbers.

These can be represented as:

• Positive integers: 1, 2, 3, 4, 5, 6, 7, ... and so on.

It is crucial to note that while all counting numbers and whole numbers include positive integers, positive integers specifically exclude zero.

From our list (0, 4, and 87), since 4 and 87 are numbers greater than zero, they qualify as positive integers. Zero is not included, as it is not positive.