Topics
Number System (Including Estimation and Approximation)
Number System
Theme 1 : Numbers
Number System(Consolidating the Sense of Numberness)
Ratio and Proportion
Theme 2 : Ratio, Proportion and Arithmetic Problems
Numbers in Indian and International Systems (With Comparison)
Estimation
Theme 3 : Algebra
Numbers in India and International System (With Comparison)
Algebra
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Place Value
Negative Numbers and Integers
Geometry
Theme 4 : Geometry
Mensuration
Theme 5 : Mensuration
Sets
Natural Numbers and Whole Numbers (Including Patterns)
Negative Numbers and Integers
Theme 6 : Statistics
Data Handling
Fractions
Number Line
Decimal Fractions
Playing with Numbers (Including H.C.F. and L.C.M.)
HCF and LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Ratio and Proportion (Including Unitary Method)
Sets
Percent (Percentage)
Idea of Speed, Distance and Time
Ratio
Fundamental Concepts (With operations on Algebraic Expressions)
Proportion (Including Word Problems)
Unitary Method
Framing Algebraic Expressions (Including Substitution and Linear Equations)
Fundamental Concepts (Including Angles and their Properties)
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Decimal Fractions
Triangles (Including Types and Properties of Triangles)
Quadrilaterals
Percent (Percentage)
Circles
Idea of Speed, Distance and Time
Symmetry
Fundamental Concepts
Constructions
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Recognition of Solids
Framing Algebraic Expressions (Including Evaluation)
Perimeter and Area of Plane Figures
Data Handling (Including Mean and Median)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Introduction
- Reading and Writing Large Numbers Using the International System
- Examples
- Real-Life Application
- Tips, Tricks, and Common Mistakes
Introduction
The world’s population, distances between planets, and large financial numbers are often written using the International System.
Learning this system helps you understand and write large numbers the way they are used globally in science, banking, and communication!
The International System: Key Points
- Digits Used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- Base-10 (Decimal) System: Value increases 10 times as you move left.
- Grouping: Large numbers are grouped into periods such as billions, millions, thousands, and ones.
- Place Value: The position of each digit determines whether it represents ones, tens, hundreds, thousands, millions, or billions.
| Periods → | Billions | Millions | Thousands | Ones | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Places ↓ | Hundred billions (HB) | Ten billion (TB) | Billions (B) | Hundred millions (HM) | Ten million (TM) | Millions (M) | Hundred thousands (HT) | Ten thousand (TT) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
Reading and Writing Large Numbers in the International System
In this system, the groups are made with periods, as shown below:
| Value | 100,000,000,000 | 10,000,000,000 | 1,000,000,000 | 100,000,000 | 10,000,000 | 1,000,000 | 100,000 | 10,000 | 1000 | 100 | 10 | 1 |
| Period | Hundred Billions (HB) | Ten Billion (T B) |
Billion | Hundred Million (HM) | Ten Million (T M) |
Million (M) |
Hundred Thousand (H Th.) |
Ten thousand (T Th) |
Thousand (Th) |
Hundreds (H) |
Tens (T) |
Ones (O) |
Reading and Writing Large Numbers in the International System:
| Periods → |
Millions | Thousands | Ones | ||||||
| Numbers ↓ | (HM) | (TM) | (M) | (HTh) | (TTh) | (Th) | (H) | (T) | (O) |
| 7456123 | 7 | 4 | 5 | 6 | 1 | 2 | 3 | ||
| 225437 | 2 | 2 | 5 | 4 | 3 | 7 | |||
| 61786425 | 6 | 1 | 7 | 8 | 6 | 4 | 2 | 5 | |
| 82854137 | 8 | 2 | 8 | 5 | 4 | 1 | 3 | 7 | |
| 743813256 | 7 | 4 | 3 | 8 | 1 | 3 | 2 | 5 | 6 |
Examples
- 7456123 = 7,456,123
= Seven million four hundred fifty-six thousand one hundred twenty-three. - 61786425 = 61,786,425
= Sixty-one million seven hundred eighty-six thousand four hundred twenty-five. - 61786425 = 61,786,425
= Sixty-one million seven hundred eighty-six thousand four hundred twenty-five. - 82854137 = 82,854,137
= Eighty-two million eight hundred fifty-four thousand one hundred thirty-seven. - 743813256 = 743,813,256
= Seven hundred forty-three million eight hundred thirteen thousand two hundred fifty-six.
Real-Life Application
-
Bank cheques, population figures, and scientific data in the news are presented in the international format, especially outside India.
-
Computer files, websites, and business reports commonly use international grouping and naming.
Tips, Tricks, and Common Mistakes
-
Commas: Always insert commas every three digits from the right in figures.
-
Reading: Never use “and” or plurals like “millions”; instead, say “one million,” “two thousand.”
-
Comparison: Unlike the Indian System, comma and period names differ beyond the thousands place.
-
Zeros: Never place zeros at the start of a number (e.g., 007,456,123).
