Number system class IX
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Type of numbers, rational and irrational numbers, decimal representation of rational and irrational numbers, venn diagram, solved examples from NCERT
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This document provides examples for solving word problems by translating English phrases into mathematical expressions. It discusses key phrases like "more than", "less than", and "times" and how they relate to addition, subtraction, and multiplication. Several geometry and consecutive number word problems are worked out step-by-step. The document emphasizes setting up variables clearly before solving and checking that the answer makes sense in the original context.
CLASS IX MATHS
God gave us natural numbers, while other types of numbers were created by humans. The German mathematician Kronecker expressed that natural numbers play a significant role in human thought. The document then defines various types of numbers - natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. It provides properties and examples for each number type. Rational numbers can be expressed as terminating or repeating decimals, while irrational numbers cannot be expressed as fractions. Together, rational and irrational numbers form the set of real numbers.
Presentation1.pptx
The document discusses different types of numbers:
1. Natural numbers, whole numbers, integers, fractions, rational numbers, irrational numbers, real numbers, imaginary numbers, prime numbers, and composite numbers.
2. It provides definitions and examples for each type of number, explaining their key properties and relationships.
3. Different types of numbers are distinguished based on their representation in decimal form and whether they can be written as ratios of integers.
ix-number system-ppt(2).pptx
This document provides learning objectives and content about rational and irrational numbers for a Class 9 mathematics lesson. It begins by defining different types of numbers - natural, whole, integers, rational, and irrational - and provides examples. It then explains rational numbers as those that can be written as fractions p/q, and irrational numbers as those that cannot be expressed as fractions. Various methods are provided for representing and finding rational numbers between two given rational numbers, as well as representing irrational numbers on the number line. Finally, the document discusses operations involving rational and irrational numbers.
November 3, 2014
- The document discusses an upcoming math final exam and provides examples to review rational equations, expressions with fractions, and formulas.
- Topics to review for the final exam include translations, order of operations, integers, and simplifying expressions. Example problems are provided to work through.
- Additional examples cover solving equations with variables on both sides, working with fractional equations, and operations with fractions and decimals such as adding, subtracting, multiplying, and dividing.
Computer Representation of Numbers and.pptx
- Computers use binary to represent numbers, where each digit is either a 1 or 0. Real numbers are approximated using floating point representation with sign, mantissa, and exponent fields.
- Integers can be stored by reserving bits for the magnitude and using the first bit to indicate sign (sign-magnitude representation) or by using two's complement representation where the most significant bit indicates sign.
- When storing numbers in memory, multiple bytes are typically used to represent integers or floating point values to support a wider range of numbers.
Abhinav
Vedic mathematics is an ancient system of mathematics discovered from the Vedas. It uses unique calculation techniques based on simple principles to solve problems mentally in arithmetic, algebra, geometry, and trigonometry. It allows problems to be solved 10-15 times faster by reducing memorization of tables and scratch work. Vedic mathematics consists of 16 sutras or formulae derived from the Vedas that simplify complex mathematical operations.
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Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
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Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
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Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
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1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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Number system class IX
- 2. TYPE OF NUMBERS Natural numbers (N): the counting numbers 1,2,3……. Whole numbers (W): Zero along with all natural numbers 0,1,2,3…. Integers (Z): Negative and positive numbers along with zero …..-3,-2,-1,0,1,2,3….. Rational numbers (Q): All integers, fractions and decimal numbers 0.25, -17, 𝟏 𝟓 , 𝟏𝟑 𝟕 , −𝟐 𝟏𝟏
- 3. RATIONAL NUMBERS Any number that can be written in the form 𝒑 𝒒 , integers , q ≠ 0. p and q have no common factors other than 1 (that is, p and q are co-prime) Do you think a natural number is a rational ? Yes, 3 can be written as 3 1 Do you think a 2.5 is a rational ? Yes, 2.5 can be written as 25 10 = 5 2
- 4. NUMBERSYSTEM
- 5. Decimal representation of rational numbers 𝟕 𝟏𝟎 = 0.7 𝟓 𝟐 = 2.5 𝟕 𝟒 = 1.75 Note: remainder is zero
- 6. Decimal representation of rational numbers 𝟐 𝟑 = 0.666…. = 0. 𝟔 𝟏 𝟕 = 0.142857142857…. = 0.𝟏𝟒𝟐𝟖𝟓𝟕 𝟏 𝟔 = 0.166666… =0.1 𝟔 Note: remainder is never zero
- 7. AmI a terminatingorrecurringdecimal??? › 𝟑𝟕 𝟐𝟓𝟎 If denominator has factors 2 and 5 only then is terminating decimal Otherwise recurring decimal or non terminating decimal 37 175 = 37 2×3×5×5 = 0.24666… =0.24 𝟔 This is recurring decimal.
- 11. CONVERTING DECIMALS TO RATIONAL NUMBERS 0.3 = 3 10 0.75 = 75 100 = 3 4 BUT WHAT IF WE NEED TO CONVERT 0.3333…. 1.2727…. 0.2353535….. into 𝑝 𝑞 form.
- 12. CONVERTING DECIMALS TO RATIONAL NUMBERS let x = 0.3333... (i) Now here is where the trick comes in. Multiply (i) by 10 10 x = 10 × (0.333...) = 3.333... Now, 3.3333... = 3 + x, since x = 0.3333... Therefore, 10 x = 3 + x Solving for x, we get 9x = 3, i.e., x = 𝟏 𝟑
- 13. CONVERTING DECIMALS TO RATIONAL NUMBERS Let x = 1.272727... Since two digits are repeating, we multiply x by 100 100 x = 127.2727... So, 100 x = 126 + 1.272727... 100x = 126 + x Therefore, 100 x – x = 126, i.e., 99 x = 126 ., x = 𝟏𝟐𝟔 𝟗𝟗 = 𝟏𝟒 𝟏𝟏
- 14. CONVERTING DECIMALS TO RATIONAL NUMBERS Let x = 0. 23535…. Over here, note that 2 does not repeat, but the block 35 repeats. Since two digits are repeating, we multiply x by 100 to get 100 x = 23.53535... So, 100 x = 23.3 + 0.23535... 100x = 23.3 + x Therefore, 99 x = 23.3 i.e., 99 x = 𝟐𝟑𝟑 𝟏𝟎 , which gives x = 𝟐𝟑𝟑 𝟗𝟗𝟎