Mathematics is a vast subject that includes so many concepts easy and difficult that might help people to do different types of analysis. Even it has so many types of numbers that are called off with different names. You all might have known about the concept of rational numbers. It is a type of real number that can even be in the fraction form but the denominator of the fraction should not be zero. There are infinite values of rational numbers.
In mathematics, a rational number is defined in the form of p/q where q ≠ 0. When the fraction will be divided, it will result in the decimal form which is also included in the rational number. There are different types of rational numbers stated below:
- The standard form of rational numbers: The standard form of the rational number can be defined when there is no common factor left between divisor and dividend. For example, 5/ 25 is a rational number. After simplifying it, the result is 1/5 which is still a rational number.
- Positive and negative rational numbers: A number that is in the form of p/q is a rational number, with a condition that q cannot be zero. The rational number can be positive or negative. If the rational number is positive both p and q are positive integers. If the rational number can be negative if any of the integers i.e. p or 1 has a negative value.
For example: Identify the following mixed fraction 3 ½ is a rational number.
Solution: The simplest form of 3 ½ is 7/2.
Here, the numerator is 7 and the denominator is 2, it is an integer that is not equal to zero. Therefore, the fraction 3 ½ is a rational number.
Rational numbers are a subset of the real number, and it has many properties of the real number system. The properties of the real number are given below:
- The results of the rational number if a case of any operation like addition, subtractions, multiplication, or division will result as the rational number only.
- If the rational number is divided or multiplied with the same factor on both numerator and denominator, it will remain the same.
- If the person adds zero to any of the rational numbers, still the number will remain the same.
- Rational numbers are closed under addition, subtraction, or even multiplication.
There are also irrational numbers that are different from rational numbers. The points of difference are stated below:
- If the fraction is having a non-zero denominator, it is considered to be a rational number. On the other hand, all the numbers that are not rational numbers become irrational numbers.
- Rational numbers can be positive, negative and even zero and are written in fraction form on the other hand the irrational numbers cannot be written as simple fractions and can only be sated in decimals. There are endless non-repeating digits after the decimal point. For example the value of ∏ = 3.142857…..
Different other concepts are deeply explained by the experts at Cuemath.com. The interested student can join the online class to clarify and no more about rational and irrational numbers.
