Topics

Number System
Rational Numbers
- Concept of Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Rational Numbers on a Number Line
- Inserting Rational Numbers Between Two Given Rational Numbers
- Method of Finding a Large Number of Rational Numbers Between Two Given Rational Numbers
Exponents
- Concept of Exponents
- Law of Exponents (For Integral Powers)
- Negative Integral Exponents
- More About Exponents
Squares and Square Root
- Concept of Square Roots
- Finding Square Root by Division Method
- Finding Square Root Through Prime Factorisation
- To Find the Square Root of a Number Which is Not a Perfect Square (Using Division Method)
- Properties of Square Numbers
Cubes and Cube Roots
- Concept of Cube Number
- Concept of Cube Root
- Concept of Cube Root
- Cube Root Through Prime Factorisation Method
Playing with Numbers
- Introduction of Playing with Numbers
- Generalized Form of Numbers
- Some Interesting Properties
- Letters for Digits (Cryptarithms)
- Divisibility by 10
- Divisibility by 2
- Divisibility by 5
- Divisibility by 3
- Divisibility by 6
- Divisibility by 11
- Divisibility by 4
Sets
- Concept of Sets
- Representation of a Set
- Cardinal Number of a Set
- Types of Sets
- Subset
- Proper Subset
- Number of Subsets and Proper Subsets of a Given Set
- Super Set
- Universal Set
- Complement of a Set
- Set Operations
- Difference of Two Sets
- Distributive Laws
- Venn Diagram
Ratio and Proportion
Percent and Percentage
- Concept of Percent and Percentage
Profit, Loss and Discount
- Concept of Discount
- Overhead Expenses
- To Find S.P., When C.P. and Gain (Or Loss) Percent Are Given
- To Find C.P., When S.P. and Gain (Or Loss) Percent Are Given
- Concept of Discount
- Computation of Tax
- Goods and Service Tax (Gst)
- Gst Comprises of
Interest
- Concept of Principal, Interest, Amount, and Simple Interest
- Concept of Compound Interest
- To Find the Principle (P); the Rate Percent (R) and the Time
- Interest Compounded Half Yearly
- Applications of Compound Interest Formula
Direct and Inverse Variations
- Variations
- Types of Variation
- Direct Variation
- Inverse Variation
- Concept for Unitary Method (With Only Direct Variation Implied)
- Concept of Arrow Method
- Time and Work
Algebra
Algebraic Expressions
- Algebraic Expressions
- Degree of Polynomial
- Product , Factor and Coefficient
- Like and Unlike Terms
- Combining like Terms
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Polynomial
- Multiplying a Polynomial by a Polynomial
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Simplification of Expressions
Identities
- Algebraic Identities
- Product of Sum and Difference of Two Terms
- Expansion Form of Numbers
- Important Formula of Expansion
- Cubes of Binomials
- Application of Formulae
Factorisation
- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Grouping
- Factorisation by Difference of Two Squares
- Factorisation of Trinomials
- Factorising a Perfect Square Trinomial
- Factorising Completely
Linear Equations in One Variable
- Simple Linear Equations in One Variable
- Solving Linear Inequations
- Linear Equation in One Variable
- Equations Reducible to the Linear Form
Linear Inequations
- Linear Equations in Two Variables
- Replacement Set and Solution Set
- Operation on of Whole Number on Number Line
- Concept of Properties
Geometry
Understanding Shapes
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Concept of Polygone
- Sum of Angles of a Polynomial
- Sum of Exterior Angles of a Polynomial
- Regular Polynomial
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
Special Types of Quadrilaterals
- Properties of Trapezium
- Properties of a Parallelogram
- Properties of Rectangle
- Properties of Rhombus
- Property: The diagonals of a square are perpendicular bisectors of each other.
Constructions
- Introduction of Constructions
- Construction of an Angle
- To Construct an Angle Equal to Given Angle
- To Draw the Bisector of a Given Angle
- Construction of Angles of 60°,30°,90° and 45°
- Construction of Bisector of a Line
- Drawing the Perpendicular Bisector of a Line Segment
- Construction of Parallel Lines
- Constructing a Quadrilateral
- Construction of Parallelograms
- Construction of a Rectangle When Its Length and Breadth Are Given.
- Construction of Rhombus
- Construction of Square
- Concept of Reflection Symmetry
Representing 3-D in 2-D
- 2dimensional Perspective of 3dimensional Objects
- Concept of Polyhedron
- Faces, Edges and Vertices
- Euler's Formula
- Concept of Polyhedron
- Nets for Building 3-d Shapes - Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism
Mensuration
Area of a Trapezium and a Polygon
- Perimeter of Triangles
- Perimeter of a Rectangle
- Perimeter of Squares
- Area of Trapezium
- Area of a Parallelogram
- Area of a Rhombus
- Area of Circle
Surface Area, Volume and Capacity
- Concept of Surface Area, Volume, and Capacity
- Surface Area of a Cuboid
- Surface Area of a Cube
- Surface Area of a Cuboid
- Surface Area of Cylinder
- Surface Area of a Cuboid
Data Handling (Statistics)
Data Handling
- Concept of Data Handling
- Collecting Data
- Frequency
- Raw Data, Arrayed Data and Frequency Distribution
- Constructing a Frequency Table
- Frequency Distribution Table
- Class Intervals and Class Limits
- Graphical Representation of Data
Probability
- Basic Ideas of Probability
- Basic Ideas of Probability

definition

Expansion of numbers: The expansion of numbers refers to the number to see the value of each digit.

notes

Expansion Form of Numbers:

The expansion of numbers refers to the number to see the value of each digit.

Number	Number Name	Expansion
58	Fifty-eight	58 = 50 + 8 = 5 × 10 + 8
259	Two hundred and fifty-nine	259 = 200 + 50 + 9 = 2 × 100 + 5 × 10 + 9.
5638	Five thousand, six hundred and thirty-eight	5638 = 5000 + 600 + 30 + 8 = 5 × 1000 + 6 × 100 + 3 × 10 + 8.
45278	Forty five thousand, two hundred and seventy-eight	45278 = 4 × 10000 + 5 × 1000 + 2 × 100 + 7 × 10 + 8.

The expansion of a 2-digit number like 58 as 58 = 50 + 8 = 5 × 10 + 8
The expansion of a 3-digit number like 259 as 259 = 200 + 50 + 9 = 2 × 100 + 5 × 10 + 9.
The expansion of 5638 is 5638 = 5000 + 600 + 30 + 8 = 5 × 1000 + 6 × 100 + 3 × 10 + 8
Here, 8 is at one's place, 3 is at ten's place, 6 is at a hundred's place and 5 is at a thousand's place.
With the number 10,000 known to us, we may extend the idea further.
We may write 5-digit numbers like 45278 = 4 × 10000 + 5 × 1000 + 2 × 100 + 7 × 10 + 8.
We say that here 8 is at one's place, 7 at ten's place, 2 at hundred's place, 5 at thousand's place, and 4 at ten thousand's place. The number is read as forty-five thousand, two hundred seventy-eight.

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Expansion Form of Numbers

Topics

Number System

Rational Numbers

Exponents

Squares and Square Root

Cubes and Cube Roots

Playing with Numbers

Sets

Ratio and Proportion

Percent and Percentage

Profit, Loss and Discount

Interest

Direct and Inverse Variations

Algebra

Algebraic Expressions

Identities

Factorisation

Linear Equations in One Variable

Linear Inequations

Geometry

Understanding Shapes

Special Types of Quadrilaterals

Constructions

Representing 3-D in 2-D

Mensuration

Area of a Trapezium and a Polygon

Surface Area, Volume and Capacity

Data Handling (Statistics)

Data Handling

Probability

definition

notes

Expansion Form of Numbers:

Number

Number Name

Expansion

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