## Rational NumbersIn mathematics, a rational number is a type of real number, which is represented in the form of p/q where q is not equal to zero. Any fractional number which doesn't have zero as its denominator is a rational number. Some examples of rational numbers are 15 / 14, 2 / 4, 6 / 7, and so on. The number "0" is also a rational number, as we can represent it in the form of 0 / 1, 0 / 2, and 0 /3. But, 1 / 0, 2 / 0, 3 / 0, etc., are not rational numbers, since the values that we get are infinite. ## What is a Rational Number?The definition of a rational number in mathematics can be given as any number which can be represented in the form of p/q where q cannot be equal to zero. Also, we can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. When the rational number (i.e., fraction) is divided, the result will be in decimal form, which can either be terminating decimal or a repeating decimal. ## How to identify rational numbers?In order to identify a rational number, - It is represented in the form of p/q, where q≠0.
- The ratio p/q can be further simplified and represented in decimal form.
- Include positive numbers, negative numbers, and zero.
- Can be expressed as a fraction.
## Different types of Rational NumbersA number is called rational only if we can write it as a fraction, where both the numerator and denominator are integers and the denominator is a non-zero number. - All rational numbers are included in the real numbers (R).
- Real numbers include the integers (Z).
- Integers involve natural numbers (N).
## The standard form of Rational NumbersThe standard form of a rational number can be defined if it's no common factors aside from one between the dividend and divisor and therefore the divisor is positive.
## Positive and Negative Rational NumbersAs we have studied earlier rational number is represented in the form of p / q, where p and q are integers. Also, q should not be zero. There is both type of natural numbers positive and negative. If the rational number is positive, both p and q are positive integers. If the rational number takes the form -(p/q), then either p or q takes the negative value. It means that:
## The Arithmetic operations on Rational NumbersIn Maths, arithmetic operations are the basic operations we perform on integers. Let us discuss here how we can perform these operations on rational numbers, say p/q and s/t.
## Multiplicative Inverse of Rational NumbersAs we already know rational numbers are represented in the form of p / q, which is a fraction, definition of the multiplicative inverse is that it is the reciprocal of the given fraction.
## Properties of Rational NumbersAs we have the knowledge that rational number is a subset of real number, rational numbers will obey the properties of the real number system. - If we do any operations on a rational number like addition multiplication, division, or subtraction, the result is always a rational number.
- There is no change in the rational number if we divide or multiply both the numerator and denominator with the same factor.
- If we add zero to a rational number, we get the same number itself.
- Rational numbers are closed under addition, subtraction, and multiplication.
## Rational Numbers and Irrational NumbersAs the name itself suggests there is a difference between rational and Irrational Numbers. A fraction that has a non-zero denominator is called a rational number. The number 2 / 3 is a rational number because it is read as integer 2 divided by integer 3. All the numbers that are not rational are known as irrational numbers.
Rational Numbers can either be positive, negative, or zero. While specifying a negative rational number, the negative sign is either in front or with the numerator of the number, which is the standard mathematical notation. An irrational number cannot be written as a simple fraction but can be represented with a decimal. It has endless non-repeating digits after the decimal point. Pi (π) = 3.142857... Euler's Number (e) = 2.7182818284590452.. √2 = 1.414213... ## How to find Rational Numbers between two Rational Numbers?There are infinite numbers of rational numbers between two rational numbers. The rational numbers between two rational numbers can be found easily using two different methods. Now, let us have a look at the two different methods.
Find out the equivalent fraction for the given rational numbers and find out the rational numbers in between them. Those numbers should be the required rational numbers.
Find out the mean value for the two given rational numbers. The mean value should be the required rational number. In order to find more rational numbers, repeat the same process with the old and the newly obtained rational numbers. Next TopicAvogadro Number |