Topics
Number System
Rational Numbers
- 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
Playing with Numbers
- Arranging the Objects in Rows and Columns
- 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 Diagrams
Ratio and Proportion
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 Equation in Two Variables
- Replacement Set and Solution Set
- Operation of Whole Numbers 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
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
Surface Area, Volume and Capacity
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
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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Series: Revisiting Place Value and Expansion Form
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