Skhandelwal said:
mathwonk said:
The definition of "rational number" is that it can be written as a fraction with numerator and denominator integers. The "ratio of the circumference of the circle to its diameter" is not a ratio of integers.Skhandelwal said:
An irrational number is a real number that cannot be expressed as a ratio of two integers. This means that it cannot be written as a fraction in the form of p/q, where p and q are integers and q is not equal to zero.
Yes, all irrational numbers are also real numbers. Real numbers include both rational and irrational numbers.
Yes, irrational numbers can be written in decimal form. However, unlike rational numbers, the decimal form of an irrational number is non-terminating and non-repeating.
Yes, there are infinitely more irrational numbers than rational numbers. In fact, the set of irrational numbers is uncountable, meaning that there is no way to list all of them in a finite amount of time.
Understanding irrational numbers is important in various fields of study, such as mathematics, physics, and engineering. They are used in calculations and equations to represent precise values that cannot be expressed as rational numbers. Additionally, irrational numbers have unique properties and patterns that have led to important discoveries in mathematics and science.