# Chapter 1 – Number System

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

You might have studied the number system in your math class. The number system or the numeral framework is the arrangement of naming or addressing numbers. In mathematics, You can find different types of number systems. Such as binary or decimal. A number system is an arrangement of writing to communicate numbers. It is the numerical documentation for addressing quantities of a given set by steadily utilising digits or different images. It provides an exceptional portrayal of each number and addresses the arithmetical construction of the figures. It likewise permits you to do arithmetical activities like expansion, deduction, and division. We hope that this article will aid you to comprehend the number system properly.

The estimation of any digit in a number can be determined by:

• The digit
• Its position in the number
• The base of the number framework

#### Rational Number

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.

#### Properties of Rational Numbers

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.

#### Exponents and Powers

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.

#### Sets Union and Intersection of Sets

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}

#### Disjoint Set

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

#### The Complement of a Set

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.

#### Laws of Exponents with Integral Powers

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

#### Conclusion

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.

#### FAQs

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
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.

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### High School Physics

• Alternating Current
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• Dual nature of Radiation and Matter
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### High School Chemistry

• Acids, Bases and Salts
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• Neural Control And Coordination
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• Plant Growth and Development
• Plant Kingdom
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• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
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• Respiration in Plants
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• Strategies for Enhancement in Food Production
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• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
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• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
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• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
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• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
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• Reaching The Age Of Adolescence
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• Separation Of Substances
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• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time