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Decimal Fractions

Topics

Basic Concepts in Geometry
Angles
Integers
Operations on Fractions
- Concept of Fractions
- Conversion Between Improper Fractions and Mixed Numbers
- Addition of Fraction
- Subtraction of Fraction
- Fraction on the Number Line
- Multiplication of Fraction
- Concept of Reciprocal or Multiplicative Inverse
- Division of Fractions
Decimal Fractions
Bar Graphs
- Concept of Bar Graph
- Drawing a Bar Graph
Symmetry
Divisibility
HCF-LCM
Equations
Ratio and Proportion
Percentage
- Basic Concept of Percentage
- Conversion between Percentage and Fraction
Profit –Loss
- Basic Concepts of Profit and Loss
- Profit or Loss as a Percentage
Banks and Simple Interest
- Bank
- Calculation of Interest
Triangles and Their Properties
Quadrilaterals
- Concept of Quadrilaterals
- Properties of a Quadrilateral
- Concept of Polygons
- Kaprekar Number
Geometrical Constructions
- Perpendicular Lines
- Drawing a Perpendicular to a Line at a Point on the Line
- Drawing a perpendicular to a line from a point outside the line
- The Perpendicular Bisector
- Drawing the perpendicular bisector of a segment using a compass.
- Carl Gauss’s Clever Trick
Three Dimensional Shapes
- Prism
- Concept of Cubes
- Concept of Cylinder
- Concept of Pyramid
- Concept of Cone
- Concept of Spheres

Definition
Positional Notation and Fraction Representation

Definition

Decimal Fractions:
A fraction whose denominator is 10, 100, 1000, or any other ten-times multiple of 10 is called a decimal fraction.
For example, `"5"/"10"`, `"68"/"100"`, `"285"/"100"`.

Positional Notation and Fraction Representation

1. Structure Based on Powers of Ten:

Each place value is ten times the value of the position to its right.

2. Examples of Place Values:

The tens place is 10 times the unit's place.
The hundreds place is 10 times the tens place.

3. Moving in the Opposite Direction (Division by Ten):

Dividing 100 by 10 results in 10.
Dividing 10 by 10 results in 1 (units place).
Dividing 1 (unit) by 10 results in 1/10 (one-tenth).

4. Introduction of the Decimal Place:

Dividing a unit into ten equal parts introduces a new place value.
This place, positioned to the right of the unit's place, is called the tenth place or the first decimal place.

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