# Decimal Representation of Rational Numbers

#### Topics

• ##### Integers
• Concept of Integers
• Multiplication and Division of Integers
• Properties of Operations on Integers
• Concept for Commutativity, Associativity, Existence of Identity
• Inverse and Distributivity
• Problem Solving Using Operations on Integers
• Statement Problems on Integers Using All Fundamental Operations.
• ##### Exponents (Including Laws of Exponents)
• Concept of Exponents
• Concept for Exponents Only Natural Numbers.
• Laws of Exponents (Through Observing Patterns to Arrive at Generalisation.)
• Concept for Application of Laws of Exponents in Simple Daily Life Problems
• ##### Unitary Method (Including Time and Work)
• Concept of Unitary Method (Including Time and Work)
• Unitary Method Continued, Consolidation, General Expression for Unitary Method .
• Relation Between Speed, Time and Distance
• ##### Simple Linear Equations (Including Word Problems)
• Simple Linear Equations in One Variable
• Simple Linear Equations in One Variable
• Concept for Inequalities
• Concept for Solution of Simple Inequalities in One Variable
• ##### Set Concepts (Some Simple Divisions by Vedic Method)
• Concept of Set Concepts
• Concept for Revision Idea of Sets
• Universal Set
• Concept for Cardinal Property of Sets
• ##### Lines and Angles (Including Construction of Angles)
• Introduction to Lines and Angles
• Concept for Pairs of Angles
• Properties of Parallel Lines
• Construction of a Line Parallel to a Given Line from a Point Outside It .
• ##### Recognition of Solids (Representing 3-d in 2-d)
• Concept of Recognition of Solids
• Faces, Edges and Vertices
• Concept for Mapping the Space Around Approximately Through Visual Estimation.
• ##### Congruency: Congruent Triangles
• Congruence of Triangles
• Concept for Congruence Through Superimposition
• Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
• Criteria for Congruence of Triangles
• ##### Probability
• Basic Ideas of Probability
• Concept for Feel of Probability Using Data Through Experiments.
• Concept for Notion of Chance
• Concept for Tabulating and Counting Occurrences
• Comparing the Observation with that for a Coin. Observing Strings of Throws, Notion of Randomness.

## Notes

### Decimal Representation of Rational Numbers:

1) Write the rational number 7/4 in decimal form.

(1) 7 = 7.0 = 7.000 (Any number of zeros can be added after the fractional part.)

(2) 1 is the quotient and 3 the remainder after dividing 7 by 4. Now we place a decimal point after the integer 1. Writing the 0 from the dividend after the remainder 3, we divide 30 by 4. As the quotient, we get now is fractional, we write 7 after the decimal point. Again we bring down the next 0 from the dividend and complete the division.

2) Write 2 1/5 in decimal form.

We shall find the decimal form of 2 1/5 = 11/5 in three different ways.

Find the decimal form of 1/5.

∴ 1/5 = 0.2

3) Write the number 2/11 in decimal form.

∴ 2/11 = 0.1818.......

2/11 = 0.bar18

4) Work out the decimal form of 5/6.

5/6 = 0.833...

∴ 5/6 = 0.8dot3

Here, a single digit or a group of digits occurs repeatedly on the right of the decimal point. This type of decimal form of a rational number is called the recurring decimal form.

If in a decimal fraction, a single-digit occurs repeatedly on the right of the decimal the point, we put a point above it as shown here. 5/6 = 0.8dot3 and if a group of digits occurs repeatedly, we show it with a horizontal line above the digits. Thus, 2/11 = 0.bar18.

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Decimal Representation of Rational Numbers [00:06:17]
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