In this blog post, we will be discussing rational numbers and irrational numbers to better understand their properties and how they differ from one another.
Rational Numbers Explained
Rational numbers are defined as any number that can be expressed in the form of a ratio (e.g., P/Q and Q ≠ 0). Examples of rational numbers include integers such as -4, 0, 1, 2, 3, 4 as well as fractions such as 3/4, 5/9, 6/11 etc. Additionally, all terminating decimals like 0.25 and 0.8 can also be expressed as a fraction and are therefore considered rational numbers.
Irrational Numbers Explained
On the other hand, irrational numbers cannot be expressed in the form of a fraction or ratio. This means that these numbers have an infinite decimal expansion without any repeating pattern. Examples of irrational numbers include √2 == 1.41421356237… , π = 3.141592653589… and e = 2.718281828459045…. All square roots of non-square natural numbers (such as √5) are irrational numbers too.
Though both rational and irrational numbers fall under the umbrella term “real number”, these two types of real number differ greatly in their properties and representation on a number line. Because rational numbers can be written as fractions whereas irrational cannot – rationals tend to be more ‘regular’ than the irregularity which characterizes irrationals on a number line!
In summary, rational numbers are those that can be expressed in the form of a ratio (e.g., P/Q where Q≠0), whereas irrationals cannot be expressed in this manner due to their infinite decimal expansion without any repeating pattern.