Topics
Rational Numbers
 Rational Numbers
 Closure Property of Rational Numbers
 Commutative Property of Rational Numbers
 Associative Property of Rational Numbers
 Distributive Property of Multiplication Over Addition for Rational Numbers
 Identity of Addition and Multiplication of Rational Numbers
 Negative Or Additive Inverse of Rational Numbers
 Reciprocal Or Multiplicative Inverse of Rational Numbers
 Rational Numbers on a Number Line
 Rational Numbers Between Two Rational Numbers
Linear Equations in One Variable
 The Idea of a Variable
 Expressions with Variables
 Concept of Equation
 Balancing an Equation
 The Solution of an Equation
 Linear Equation in One Variable
 Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
 Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
 Solving Equations Having the Variable on Both Sides
 Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
 Reducing Equations to Simpler Form
 Equations Reducible to the Linear Form
Understanding Quadrilaterals
 Concept of Curves
 Different Types of Curves  Closed Curve, Open Curve, Simple Curve.
 Concept of Polygons  Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
 Classification of Polygons
 Angle Sum Property of a Quadrilateral
 Interior Angles of a Polygon
 Exterior Angles of a Polygon and Its Property
 Concept of Quadrilaterals  Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
 Properties of Trapezium
 Properties of Kite
 Properties of a Parallelogram
 Properties of Rhombus
 Property: The Opposite Sides of a Parallelogram Are of Equal Length.
 Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
 Property: The adjacent angles in a parallelogram are supplementary.
 Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
 Property: The diagonals of a rhombus are perpendicular bisectors of one another.
 Property: The Diagonals of a Rectangle Are of Equal Length.
 Properties of Rectangle
 Properties of a Square
 Property: The diagonals of a square are perpendicular bisectors of each other.
Practical Geometry
 Introduction to Practical Geometry
 Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
 Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
 Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
 Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
 Some Special Cases
Data Handling
 Concept of Data Handling
 Interpretation of a Pictograph
 Interpretation of Bar Graphs
 Drawing a Bar Graph
 Interpretation of a Double Bar Graph
 Drawing a Double Bar Graph
 Organisation of Data
 Frequency Distribution Table
 Graphical Representation of Data as Histograms
 Concept of Pie Graph (Or a Circlegraph)
 Interpretation of Pie Diagram
 Chance and Probability  Chance
 Basic Ideas of Probability
Squares and Square Roots
 Concept of Square Number
 Properties of Square Numbers
 Some More Interesting Patterns of Square Number
 Finding the Square of a Number
 Concept of Square Roots
 Finding Square Root Through Repeated Subtraction
 Finding Square Root Through Prime Factorisation
 Finding Square Root by Division Method
 Square Root of Decimal Numbers
 Estimating Square Root
Cubes and Cube Roots
Comparing Quantities
 Concept of Ratio
 Concept of Percent and Percentage
 Increase Or Decrease as Percent
 Concept of Discount
 Estimation in Percentages
 Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
 Sales Tax, Value Added Tax, and Good and Services Tax
 Concept of Principal, Interest, Amount, and Simple Interest
 Concept of Compound Interest
 Deducing a Formula for Compound Interest
 Rate Compounded Annually Or Half Yearly (Semi Annually)
 Applications of Compound Interest Formula
Algebraic Expressions and Identities
 Algebraic Expressions
 Terms, Factors and Coefficients of Expression
 Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
 Like and Unlike Terms
 Addition of Algebraic Expressions
 Subtraction of Algebraic Expressions
 Multiplication of Algebraic Expressions
 Multiplying Monomial by Monomials
 Multiplying a Monomial by a Binomial
 Multiplying a Monomial by a Trinomial
 Multiplying a Binomial by a Binomial
 Multiplying a Binomial by a Trinomial
 Concept of Identity
 Expansion of (a + b)2 = a2 + 2ab + b2
 Expansion of (a  b)2 = a2  2ab + b2
 Expansion of (a + b)(a  b)
 Expansion of (x + a)(x + b)
Visualizing Solid Shapes
Mensuration
Exponents and Powers
Direct and Inverse Proportions
Factorization
 Factors and Multiples
 Factorising Algebraic Expressions
 Factorisation by Taking Out Common Factors
 Factorisation by Regrouping Terms
 Factorisation Using Identities
 Factors of the Form (x + a)(x + b)
 Dividing a Monomial by a Monomial
 Dividing a Polynomial by a Monomial
 Dividing a Polynomial by a Polynomial
 Concept of Find the Error
Introduction to Graphs
 Concept of Bar Graph
 Interpretation of Bar Graphs
 Drawing a Bar Graph
 Concept of Double Bar Graph
 Interpretation of a Double Bar Graph
 Drawing a Double Bar Graph
 Concept of Pie Graph (Or a Circlegraph)
 Graphical Representation of Data as Histograms
 Concept of a Line Graph
 Linear Graphs
 Linear Graphs
 Some Application of Linear Graphs
Playing with Numbers
Notes
Comparing Very Large and Very Small Numbers:
Before comparing very large or small numbers, We convert them to their standard exponential form and then divide them.

If two numbers in standard form have the same power of 10, then the number with the larger factor is greater.
For example, 8.72 × 10^{24} < 9.4326 × 10^{24}. 
If two numbers in standard form have the same factor, then the number with the larger power of 10 will be greater.
For example, 8.72 × 10^{8} > 8.72 × 10^{4}. 
If two numbers in standard form have different factors and the different power of 10, then the number with the higher power of ten (i.e., the larger exponent) is the larger number.
For example, 8.72 × 10^{24} > 9.4326 × 10^{23}.
Shaalaa.com  Comparing Very Large and Very Small Numbers
Related QuestionsVIEW ALL [22]
Astronomy The table shows the mass of the planets, the sun and the moon in our solar system.
Celestial Body 
Mass (kg)  Mass (kg) Standard Notation 
Sun  1,990,000,000,000,000,000,000,000,000,000  1.99 × 10^{30} 
Mercury  330,000,000,000,000,000,000,000  
Venus  4,870,000,000,000,000,000,000,000  
Earth  5,970,000,000,000,000,000,000,000  
Mars  642,000,000,000,000,000,000,000,000,000  
Jupiter  1,900,000,000,000,000,000,000,000,000  
Saturn  568,000,000,000,000,000,000,000,000  
Uranus  86,800,000,000,000,000,000,000,000  
Neptune  102,000,000,000,000,000,000,000,000  
Pluto  12,700,000,000,000,000,000,000  
Moon  73,500,000,000,000,000,000,000 
(a) Write the mass of each planet and the Moon in scientific notation.
(b) Order the planets and the moon by mass, from least to greatest.
(c) Which planet has about the same mass as earth?
Investigating Solar System The table shows the average distance from each planet in our solar system to the sun.
Planet  Distance from Sun (km) 
Distance from Sun (km) Standard Notation 
Earth  149,600,000  
Jupiter  778,300,000  
Mars  227,900,000  
Mercury  57,900,000  
Neptune  4,497,000,000  
Pluto  5,900,000,000  
Saturn  1,427,000,000  
Uranus  2,870,000,000  
Venus  108,200,000 
(a) Complete the table by expressing the distance from each planet to the Sun in scientific notation.
(b) Order the planets from closest to the sun to farthest from the sun
This table shows the mass of one atom for five chemical elements. Use it to answer the question given.
Element  Mass of atom (kg) 
Titanium  7.95 × 10^{–26} 
Lead  3.44 × 10^{–25} 
Silver  1.79 × 10^{–25} 
Lithium  1.15 × 10^{–26} 
Hydrogen  1.674 × 10^{–27} 
(a) Which is the heaviest element?
(b) Which element is lighter, Silver or Titanium?
(c) List all five elements in order from lightest to heaviest.