# Chapter 1 – Number System

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

Introduction

The numeral scheme, that you also know as the number system, identifies and displays numbers. In mathematics, there are several different kinds of number structures, such as binary and decimal. Let’s understand this system in detail.

A number system is a way of expressing numbers by writing. It is a mathematical notation for consistently representing numbers from a specified range 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 numbers
• Its position
• The number system’s base

#### Multiplication and Division of Integers

• Multiplication
RULE 1: A positive integer compounded by a negative integer produces a negative integer.
RULE 2: When multiplying two positive integers, the result is positive.
RULE 3: When multiplying two negative integers, the answer is positive.
• Division
RULE 1: A positive integer’s quotient with a negative integer is negative.
RULE 2: When two positive integers are quotients, the result is positive.
RULE 3: When two negative integers are multiplied together, the quotient is positive.

#### Properties of Operations on Integers

Integers have a few properties that dictate how they are used. Many equations may be solved using these rules or properties. Any positive or negative number, even zero, is an integer. The properties of these integers can assist in easily simplifying and addressing a sequence of integer operations.

The following are the five significant properties of operation for integers:

• Closure property
• Associative property
• Commutative property
• Distributive property
• Identity property

#### Introduction to Rational Numbers

Any number can be expressed as p/q, where q≠0 is a rational number in mathematics. We may also classify any fraction as a rational number if the denominator and numerator are both integers and the denominator is not equal to zero. As a rational number (i.e., a fraction) is split, the output is in decimal form and may be ending or repeating.

Check the criteria below to see whether a number is logical or not.

• It’s written as p/q, where q≠0.
• The p/q ratio can be condensed further and displayed in decimal form.

#### Decimal Representation of Rational Numbers

Rather than expressing rational numbers as fractions, they may be expressed in decimal form. They can conveniently be converted to decimals by dividing the numerator “p” by the denominator “q” (as rational numbers are written in the form p/q).

A terminating or non-terminating, repeating decimal may be used to express a rational number.

Compared to improper rational fractions, the representation of rational numbers in decimal fractions allows calculations to be more straightforward.

#### Fractions

A fraction is a numerical value that denotes the components of a larger whole. If a number is separated into four sections, it is represented 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 several instances of a fraction as an operator that you can find in daily life.

#### Types of Fractions

They are as follows:

• Proper fractions
Proper fractions have a numerator that is smaller than the denominator. Since “numerator < denominator,” 8/9 is a proper fraction.
• Improper fractions
A fraction with an incorrect numerator is one in which the numerator is greater than the denominator. 9/8, for example, is an improper fraction since the “denominator” is smaller than the “numerator.”
• Mixed fractions
A mixed fraction comprises two parts: an integer and a proper fraction. A mixed fraction is also known as a mixed numeral.
• Like fractions
Like fractions are fractions that are related or equal. Take the fractions 4/8 and 2/4, for example; they are similar because you get the same fraction when you simplify them mathematically.
• Unlike fractions
Those that are dissimilar are unlike fractions. 3/7 and 1/3, for example, are diametrically opposed fractions.
• Equivalent fractions
If one of the two fractions is identical to the other after simplification, the two fractions are equivalent. 2/3 and 4/6, for example, are equivalent fractions.

#### Conclusion

In this chapter, we learned about number systems. We learned about fractions and the reciprocal of a fraction. We can further use this knowledge for problem-solving using operations.

#### FAQs

1. What are fractions, precisely?
Fractions are integer quantities that are a percentage 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.
2. What’s the correct way to solve fractions?
When adding or subtracting fractions, we must first decide if the denominators are the same or different. When the denominators are the same, we may add or remove the numerators while leaving the denominator the same. However, if the denominators vary, we must find the LCM to reduce them.
3. Is the number 0 rational?
Yes, 0 is a rational number since it is an integer we can write in various ways, including 0/1, 0/2, and 0/3, where b is a non-zero integer. It can be expressed in the following way: p/q = 0/1. As a result, we may claim that 0 is a rational number.
4. Is seven a rational number?
Since it can be written as a ratio, such as 7/1, 7 is a rational number.
5. What is the significance of the number system?
The number scheme helps to depict numbers in a minimal symbol range.

The MSVgo app is your one-stop solution for learning the number system through simple, interactive, and explanatory visualizations. Download the app on the iOS App Store or Google Play Store today!

### 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
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• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
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• Mole Concept and Stoichiometry
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• Organic Chemistry – Basic Principles
• Periodic Classification of Elements
• Physical and Chemical Changes
• Physical and Chemical Properties of Water
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• 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