Rational numbers are in the p/q structure where q is not equal to 0. Any division with non-zero denominators is a rational number. So we can easily draw inferences that 0 is also a rational number. You can identify the rational number in two ways:

• If it is represented as p/q, that means q≠0.
• If p/q can be simplified and addressed in decimal structure.

Since a rational number is a part of a real number, it will have properties similar to real numbers. The following are the properties of rational numbers:

• The outcomes are consistently a rational number if we multiply, add, or deduct any two rational numbers.
• A rational number will be the same if we divide or multiply both the numerator and denominator with a similar factor.
• If a zero is added to a rational number, we will get a similar number itself.
• If we add, subtract or multiply, the rational number is closed.

For expressing large numbers or small numbers quickly and simply, exponents and powers are used. For example, if we wish to show 4x4x4 easily and simply, we can express it as 43. Here 4 is the base, and 3 is an exponent. It is to be noted here that if a base number is one, the result is 1.

If there are two sets A and B, the convergence of A and B is the subset of universal set U, which comprises components basic to both A and B. It can be represented by ‘∩’. This activity is addressed by:

A∩B = {x : x ∈ A and x ∈ B}

When a pair of sets do not have any common elements, it is called a disjoint set. When the convergence of two sets is a null or void set, at that point, they are called disjoint sets. Subsequently, if A and B are two disjoint sets, then:

A ∩ B = ϕ

If U is a universal set and A is part of U, then the complement of A is the arrangement of all individuals from the all-inclusive set U, not A’s components.

A′ = {x : x ∈ U and x ∉ A}

On the other hand, the distinction of the all universal set U and the subset A provides us with the complement of set A.

Exponents are utilized to show rehashed augmentation of a number by itself. The laws of exponents are utilized to take care of numerous numerical issues. The following are the crucial laws of exponents:

• am×an = am+n
• am/an = am-n
• (am)n = amn
• an/bn = (a/b)n
• a0 = 1
• a-m = 1/am
• a1n=a

The number system is an easy yet crucial concept that is also used in computers. It has many mathematical applications, and the most widely recognized of them are decimal, binary, octal, and hexadecimal.

1. What are the types of Number systems?
   There are mainly four types of number systems:
   • Decimal number system
   • Binary number system
   • Octal number system
   • Hexadecimal number system
     
2. What is the importance of the number system?
   A number framework is characterized as an arrangement of writing to communicate numbers. It is the numerical documentation for addressing quantities of a given set by utilizing digits or different symbols reliably.
3. The distinction between the squares of two continuous odd numbers is divisible by __.
   The distinction between the squares of two continuous odd numbers is divisible by 8.
   
   
4. What is a computer numerical system?
   When we type any letter or word, the PC interprets them into numbers since PCs can see just numbers. A PC can see a couple of images called digits, and these images depict various qualities relying upon the position they hold in the number. The binary number framework is utilized in the PC.
5. How to solve number system questions quickly?
   You have to practice number system questions a lot. Remember and learn the formulas. The topic is easy; it just requires conceptual clarity. You can even practice mock test series.