Describe the relationship between whole numbers, integers, and rational numbers.
Whole numbers are a set of numbers that includes all the positive counting numbers (1, 2, 3, ...), and zero.
Integers, on the other hand, are a set of numbers that includes all whole numbers (positive counting numbers and zero), as well as their negatives (-1, -2, -3, ...).
Rational numbers include both whole numbers and integers, but they also include fractions and decimals that can be written as a ratio (a/b) where "a" and "b" are integers and "b" is not equal to zero. This means that rational numbers can be expressed as a fraction or a decimal that either terminates or repeats.
In summary, the relationship is that the set of whole numbers is a subset of integers, and the set of integers is a subset of rational numbers.
The relationship between whole numbers, integers, and rational numbers can be understood as a hierarchy or a progression of number sets that become increasingly inclusive.
1. Whole Numbers: Whole numbers include all the natural or counting numbers like 0, 1, 2, 3, and so on. They do not include any negative numbers or fractions.
2. Integers: Integers include all the whole numbers as well as their negative counterparts. In other words, integers include positive numbers, negative numbers, and zero (0). It can be represented by the symbol Z.
So, the set of integers includes -3, -2, -1, 0, 1, 2, 3, and so on.
3. Rational Numbers: Rational numbers include all the integers as well as fractions and decimals (which can be expressed as fractions). A rational number is any number that can be expressed as the ratio of two integers. The set of rational numbers is denoted by the symbol Q.
For example, 1/2, 3/4, -5/7, 0.25, -1.5, etc., are all rational numbers.
In summary, the relationship between whole numbers, integers, and rational numbers is that whole numbers are a subset of integers, and integers are a subset of rational numbers. This means that all whole numbers are integers, and all integers are rational numbers, but not all rational numbers are integers, and not all integers are whole numbers.