The Number System Unit Test
Math 8 Q1 (Pre-Algebra) / The Number System
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.(4 points)
The relationship between rational numbers and whole numbers is that all whole numbers can be considered rational numbers. However, not all rational numbers are whole numbers.
Whole numbers are integers greater than or equal to zero (0, 1, 2, 3, ...). They do not include any fractions, decimals, or negatives.
Rational numbers, on the other hand, include whole numbers as well as fractions and decimals. A rational number can be expressed as a ratio or fraction of two integers, where the denominator is not zero. For example, 3, 0.5, -2, and ⅔ are all rational numbers.
Therefore, all whole numbers such as 0, 1, 2, 3, etc., can be considered rational numbers since they can be written as fractions with a denominator of 1 (e.g., 0 = 0/1, 1 = 1/1, 2 = 2/1). However, not all rational numbers are whole numbers. For instance, 0.5 and ⅔ cannot be expressed as whole numbers.
In conclusion, while all whole numbers are rational numbers, not all rational numbers are whole numbers.
The relationship between rational numbers and whole numbers is that all whole numbers are rational numbers, but not all rational numbers are whole numbers.
Whole numbers are the set of numbers that start from zero and include all positive integers. Examples of whole numbers are 0, 1, 2, 3, 4, and so on.
On the other hand, rational numbers are the set of numbers that can be expressed as a fraction or a ratio of two integers. This includes whole numbers as well as fractions and decimals. Examples of rational numbers that are not whole numbers are 1/2, 3/4, 0.25, and -2.5.
To summarize, all whole numbers are rational numbers because they can be expressed as a fraction with a denominator of 1. However, not all rational numbers are whole numbers because rational numbers include fractions and decimals that are not part of the set of whole numbers.