Topics
Integers
- Concept for Natural Numbers
- Concept for Whole Numbers
- Negative and Positive Numbers
- Concept of Integers
- Representation of Integers on the Number Line
- Concept for Ordering of Integers
- Addition of Integers
- Subtraction of Integers
- Properties of Addition and Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Product of Three Or More Negative Integers
- Closure Property of Multiplication of Integers
- Commutative Property of Multiplication of Integers
- Multiplication of Integers with Zero
- Multiplicative Identity of Integers
- Associative Property of Multiplication of Integers
- Distributive Property of Multiplication of Integers
- Making Multiplication Easier of Integers
- Division of Integers
- Properties of Division of Integers
Fractions and Decimals
- Concept of Fractions
- Fraction and its Types
- Concept of Proper Fractions
- Improper Fraction and Mixed Fraction
- Concept of Equivalent Fractions
- Like and Unlike Fraction
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of a Fraction by a Whole Number
- Fraction as an Operator 'Of'
- Multiplication of Fraction
- Division of Fractions
- Concept of Reciprocal or Multiplicative Inverse
- Problems Based on Fraction
- The Decimal Number System
- Comparing Decimal Numbers
- Addition of Decimal Fraction
- Subtraction of Decimal Numbers
- Multiplication of Decimal Fractions
- Multiplication of Decimal Numbers by 10, 100 and 1000
- Division of Decimal Numbers by 10, 100 and 1000
- Division of Decimal Fractions
- Division of a Decimal Number by Another Decimal Number
- Problems Based on Decimal Numbers
Data Handling
Simple Equations
Lines and Angles
- Concept of Points
- Concept of Line
- Concept of Line Segment
- Concept of Angle
- Complementary Angles
- Supplementary Angles
- Concept of Angle
- Concept of Linear Pair
- Concept of Vertically Opposite Angles
- Concept of Intersecting Lines
- Introduction to Parallel Lines
- Pairs of Lines - Transversal
- Pairs of Lines - Angles Made by a Transversal
- Pairs of Lines - Transversal of Parallel Lines
The Triangle and Its Properties
- Concept of Triangles
- Classification of Triangles (On the Basis of Sides, and of Angles)
- Classification of Triangles based on Sides- Equilateral, Isosceles, Scalene
- Classification of Triangles based on Sides- Equilateral, Isosceles, Scalene
- 3. Classification of Triangles based on Angles: Acute-Angled, Right-Angled, Obtuse-Angled
- 3. Classification of Triangles based on Angles: Acute-Angled, Right-Angled, Obtuse-Angled
- Median of a Triangle
- Altitudes of a Triangle
- Exterior Angle of a Triangle and Its Property
- Angle Sum Property of a Triangle
- Some Special Types of Triangles - Equilateral and Isosceles Triangles
- Sum of the Lengths of Two Sides of a Triangle
- Right-angled Triangles and Pythagoras Property
Comparing Quantities
- Concept of Ratio
- Concept of Equivalent Ratios
- Concept of Proportion
- Concept of Unitary Method
- Basic Concept of Percentage
- Conversion between Percentage and Fraction
- Converting Decimals to Percentage
- Conversion between Percentage and Fraction
- Converting Percentages to Decimals
- Estimation in Percentages
- Interpreting Percentages
- Converting Percentages to “How Many”
- Ratios to Percents
- Increase Or Decrease as Percent
- Basic Concepts of Profit and Loss
- Profit or Loss as a Percentage
- Calculation of Interest
Congruence of Triangles
Rational Numbers
- Rational Numbers
- Equivalent Rational Number
- Positive and Negative Rational Numbers
- Rational Numbers on a Number Line
- Rational Numbers in Standard Form
- Comparison of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
Perimeter and Area
- Mensuration
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangles
- Perimeter of Polygon
- Concept of Area
- Area of Square
- Area of Rectangle
- Triangles as Parts of Rectangles and Square
- Generalising for Other Congruent Parts of Rectangles
- Area of a Parallelogram
- Area of a Triangle
- Circumference of a Circle
- Area of Circle
- Conversion of Units
- Problems based on Perimeter and Area
Algebraic Expressions
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Like and Unlike Terms
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Evaluation of Algebraic Expressions by Substituting a Value for the Variable.
- Use of Variables in Common Rules
Practical Geometry
- Construction of a Line Parallel to a Given Line, Through a Point Not on the Line
- Construction of Triangles
- Constructing a Triangle When the Length of Its Three Sides Are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
- Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion)
- Constructing a Right-angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion)
Exponents and Powers
- Concept of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Decimal Number System Using Exponents and Powers
- Crores
Symmetry
Visualizing Solid Shapes
- Introducing crores
- A standard form of large numbers
Introducing Crores:
The largest seven-digit number is 99,99,999. On adding the number 1 to it, we get the smallest eight-digit number, 1,00,00,000. This figure is interpreted as "one crore." The new place created to write this number is called the ‘crores’ place.
Reading and Writing Eight-Digit Numbers:
(1) 8,45,12,706: Eight crore forty-five lakh twelve thousand seven hundred and six
(2) 5,61,63,589: Five crore sixty-one lakh sixty-three thousand five hundred and eighty-nine.
Formation of large numbers:
9 + 1 = 10
99 + 1 = 100
999 + 1 = 1,000
9,999 + 1 = 10,000
99,999 + 1 = 1,00,000
9,99,999 + 1 = 10,00,000
99,99,999 + 1 = 1,00,00,000
Reading and Writing Large Numbers
Number | TCr | Cr | TLakh | Lakh | TTh | Th | H | T | O | Number Name |
65,32,75,829 | 6 | 5 | 3 | 2 | 7 | 5 | 8 | 2 | 9 | Sixty-five crore thirty two lakh seventy-five thousand eight hundred twenty-nine |
A standard form of large numbers
Expressing Large Numbers in the Standard Form:
Any number can be expressed as a decimal number between 1.0 and 10.0, including 1.0 multiplied by a power of 10. Such a form of a number is called its standard form.
- Step 1: First of all, count the number of digits from the left, leaving only the first digit.
- Step 2: To write it in exponent or standard form, write down the first digit.
- Step 3: If there are more digits in the number, then put a decimal after the first digit and then write down the other digits until the zero comes.
- Step 4: Now place a multiplication sign and then write down the counted digits in the first step as the exponent to the base number 10.
150,000,000,000 = 1.5 × 1011
While converting a huge number like 150,000,000,000 into standard form, we need to move the decimal place towards the left, and when we do so, the exponent will be positive. Thus,
59 = 5.9 × 10 = 5.9 × 101
590 = 5.9 × 100 = 5.9 × 102
5900 = 5.9 × 1000 = 5.9 × 103
5900 = 5.9 × 10000 = 5.9 × 104 and so on.
Thus,
5,985 = 5.985 × 1,000 = 5.985 × 103 is the standard form of 5,985.
Note, 5,985 can also be expressed as 59.85 × 100 or 59.85 × 102. But these are not the standard forms of 5,985. Similarly,
5,985 = 0.5985 × 10,000 = 0.5985 × 104 is also not the standard form of 5,985.
Examples:
The distance of the Sun from the centre of our galaxy, i.e., 300,000,000,000,000,000,000 m, can be written as 3.0 × 100,000,000,000,000,000,000 = 3.0 × 1020m
Mass of the Earth = 5,976,000,000,000,000,000,000,000 kg = 5.976 × 1024 kg.
Example
Express the following number in the standard form: 5985.3
5985.3 = 5.9853 × 1000 = 5.9853 × 103.
Example
Express the following number in the standard form: 65,950
65,950 = 6.595 × 10,000 = 6.595 × 104.
Example
Express the following number in the standard form: 3,430,000
3,430,000 = 3.43 × 1,000,000 = 3.43 × 106.
Example
Express the following number in the standard form: 70,040,000,000
70,040,000,000 = 7.004 × 10,000,000,000 = 7.004 × 1010.
Video Tutorials
Shaalaa.com | Number & Units- Part 1 (CBSE 6th STD)
Series: Large Numbers in Practice
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