Describe the relationship between whole numbers, integers, and rational numbers
Whole numbers are a set of numbers that includes all the natural numbers (positive whole numbers) along with zero. Integers, on the other hand, consist of whole numbers (including zero) as well as their negatives. So, integers are a superset of whole numbers.
Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. This includes all integers as they can be written with a denominator of 1. So, integers are a subset of rational numbers.
In summary, the relationship between these number sets can be described as follows:
- Whole numbers are a subset of integers.
- Integers are a subset of rational numbers.
The relationship between whole numbers, integers, and rational numbers is as follows:
1. Whole numbers: Whole numbers are non-negative numbers that do not have decimal or fractional parts. They include the numbers 0, 1, 2, 3, and so on. Whole numbers are a subset of integers.
2. Integers: Integers include all the whole numbers, both positive and negative, along with zero. They consist of numbers like -3, -2, -1, 0, 1, 2, 3, and so on. Integers are a subset of rational numbers.
3. Rational numbers: Rational numbers are numbers that can be represented as a fraction or a ratio of two integers. They can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. Rational numbers include integers, as any integer can be expressed as itself divided by 1. Examples of rational numbers are -3/4, 1/2, 5/3, etc.
In summary, whole numbers are a subset of integers, and integers are a subset of rational numbers. This means that every whole number is an integer, and every integer is a rational number.
The relationship between whole numbers, integers, and rational numbers is as follows:
Whole numbers: Whole numbers are a set of numbers that includes all the natural numbers (counting numbers), along with zero. They are typically denoted by the symbol "W". The set of whole numbers can be represented as {0, 1, 2, 3, 4, ...}.
Integers: Integers are a broader set of numbers that includes not only the whole numbers but also their negatives. The integers are typically denoted by the symbol "Z". The set of integers can be represented as {..., -3, -2, -1, 0, 1, 2, 3, ...}.
Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers, where the numerator and denominator can be any integer except for zero. Rational numbers are typically denoted by the symbol "Q". The set of rational numbers includes both integers and fractions. For example, 1, -2, 3/4, -5/2, and 0.333... are all rational numbers.
Therefore, we can say that whole numbers are a subset of integers, and integers are a subset of rational numbers. In other words, every whole number is an integer, and every integer is a rational number. However, not every rational number is an integer, and not every integer is a whole number.