# Chapter 1 – Number System

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

Introduction

The numeral scheme, also known as the number system, identifies displays numbers and plays with numbers. There are several different kinds of number structures in mathematics, such as binary, decimal, etc.

#### What is the Mathematical Number System?

A number structure is a way of expressing numbers by writing. It is a mathematical notation for consistently representing numbers from a particular series using digits or other symbols. It reflects the arithmetic and algebraic structure of the figures and offers a specific representation for each number. We may also do mathematical operations like addition, subtraction, and division with it.

The meaning of any digit in a number can be calculated using the following formula:

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

#### Natural Numbers and Whole Numbers

Natural numbers are a set of positive integers ranging from 1 to infinity, besides fractional and decimal numbers. They are sometimes classified as number counts.

Natural number types include:

• Prime numbers
• Even and Odd numbers
• Composite numbers
• Co-prime numbers
• Perfect numbers

Whole numbers are a set of positive integers that include 0 and range from 0 to infinity. They also exclude the fractional and decimal parts.

#### Fractions

A fraction is a numerical value that denotes the components of a larger whole. If a number is separated into four bits, it is denoted by the symbol x/4. As a result, the fraction x/4 denotes 1/4th of the integer x. Fractions have a significant role in our everyday lives. There are many instances of fractions that you can see in everyday life. We have to share the delicious pizza with our friends and family, whether we want to or not. Four slices for three participants.

#### Fractions by Type

Fractions are classified into various forms based on the properties of the numerator and denominator. They are as follows:

• Like fractions
• Unlike fractions
• Equivalent fractions
• Mixed fractions
• Improper fractions
• Proper fractions

#### Comparison of Fractions

A fraction is a portion of a whole or a set of equivalent components. It is often necessary to equate two fractions to determine which is greater or smaller. There are two techniques for comparing fractions in mathematics.

1. Using the Decimal Method to Compare Fractions
Each fraction is translated to a decimal using the decimal system by dividing the numerator by the denominator. The decimal value is compared after separation.
2. Using the Same Denominator Method to Compare Fractions
As we all know, any fraction includes two terms: the numerator and the denominator. The numerator is at the top, while the denominator is at the bottom. Consider the fraction 3/4 as an example. The numerator is 3, and the denominator is 4.

#### Operations on Fractions

While arithmetic includes several other updated operations, the core operations are addition and subtraction, division, and multiplication.

The addition is one of the most fundamental arithmetic processes. The addition incorporates two or more ideas into a common word at the most basic shape.
2. Subtraction
Subtraction is known as the antithesis of inclusion. It calculates the discrepancy between two numbers, i.e. the subtrahend minus the minuend. The distinction is positive if the minuend is larger than the subtrahend. The answer is negative if the minuend is smaller than the subtrahend, and 0 if the numbers are equivalent.
3. Multiplication
Multiplication often transforms two quantities, such as addition and subtraction, into a single value referred to as the element. The multiplicand and multiplier, or both as variables, are the two initial values.The multiplication of two numbers is written as ab or a x b. It is sometimes represented as a*b (asterisk) in machine languages where only characters present on keyboards are used.
4. Division
It is the opposite of differentiation. It finds the quotient of two numbers, which is the dividend separated by the divisor. If the dividend is greater than the divisor for every well-defined positive integer, the quotient is greater than 1; else, it is less than 1.

#### Simplification of Brackets

The terms within the brackets may be simplified explicitly. We may conduct division, multiplication, addition, and subtraction in the order specified within the bracket. This concept is a part of the BODMAS rule.

#### Conclusion

In this chapter, we learned about the basics of number systems. We gathered knowledge of fractions and their related concepts.

#### FAQs

1. What are the different types of number systems?
The number structure is nothing more than a way of representing or expressing quantities. The decimal number system, binary number system, octal number system, and hexadecimal number system are the most widely employed number systems.
2. What is the significance of the number system?
The number scheme aids in representing numbers in a limited symbol range. In general, computers use binary numbers 0 and 1 to simplify calculations and reduce the amount of circuitry required, resulting in the least amount of space, energy usage, and expense.
3. Explain fractions.
Fractions are integer quantities that are a fraction of a whole number. As a number or an object is separated into equivalent sections, each component becomes a fraction of the total. Where an is the numerator and b is the denominator, a fraction is written as a/b.
4. In math, what are the three kinds of fractions?Mixed fractions, improper fractions, and proper fractions are the three groups of fractions of mathematics.
5. What is the concept of a unit fraction?
A division with a unit(one) numerator is known as a unit fraction.

### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
• Oscillations
• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
• Specific and Latent Heats
• Spherical Mirrors
• Static Electricity
• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
• Atoms And Molecules
• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
• Chemical Equilibria
• Chemical Kinetics
• Chemical Reactions And Equations
• Chemical Reactions and Their Mechanisms
• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
• Electrolysis
• Elements, Compounds and Mixtures
• Environmental Chemistry
• Equilibrium
• Ethers and Carbonyl compounds
• Haloalkanes and Haloarenes
• Hydrocarbons
• Hydrogen
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• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
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• Metallurgy
• Metals And Non-Metals
• Mole Concept and Stoichiometry
• Natural Resources
• Organic Chemistry – Basic Principles
• Periodic Classification of Elements
• Physical and Chemical Changes
• Physical and Chemical Properties of Water
• Polymers
• Preparation, Properties and Uses of Compounds
• Principles and Processes of Isolation of Elements
• Redox Reactions
• Relative Molecular Mass and Mole
• States of Matter
• Structure Of The Atom
• Study of Compounds
• Study of Gas Laws
• Study of Representative Elements
• Surface Chemistry
• The d-block and f-block elements
• The Gaseous State
• The p-Block Elements
• The Periodic Table
• The s-Block Elements
• The Solid State
• Thermodynamics

### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
• Biofertilizers
• Biological Classification
• Biomedical Engineering
• Biomolecules
• Biotechnology and its Applications
• Biotic Community
• Body Fluids and Circulation
• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
• Cellular Respiration
• Chemical Coordination and Integration
• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
• Environmental Issues
• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
• Human Eye And Colourful World
• Human Health and Disease
• Human Population
• Human Reproduction
• Hygiene
• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
• Kingdom Protista
• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• 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
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• 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
• Hydrogen
• 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
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• 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