Numebr system
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This document discusses different types of numbers. It begins with counting numbers which start from 1 and have no largest number. Natural numbers also start from 1 and are infinite. Whole numbers include 0 and are also infinite. Integers include both positive and negative numbers and have an equal and opposite number for every integer. Rational numbers are numbers that can be represented as fractions. Real numbers include both rational numbers like fractions as well as irrational numbers like pi which have non-terminating, non-repeating decimals. The real number set contains all other number sets.
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NUMBER SYSTEM
This document discusses different types of number systems. It begins by introducing natural numbers, which are counting numbers formed by repeated addition of 1. Whole numbers include all natural numbers and 0. Integers extend whole numbers infinitely in both the positive and negative directions. Rational numbers are numbers that can be written as fractions p/q where p and q are integers. Irrational numbers have non-repeating decimal expansions and cannot be written as fractions. Real numbers include all rational and irrational numbers and are represented on the number line. Methods for finding rational numbers between two given numbers and representing different types of numbers on the number line are also described.
Number Systems
Real numbers include rational numbers like integers and fractions as well as irrational numbers like square roots and pi. Real numbers can be represented on a continuous number line and include both countable and uncountable infinite numbers. Real numbers have the properties of a field where they can be added, multiplied, and ordered on the number line in a way compatible with these operations. Rational numbers are numbers that can be represented as fractions of integers, and they include integers, whole numbers, and natural numbers. Irrational numbers cannot be represented as fractions.
Number system for class Nine(IX) by G R Ahmed TGT(Maths) at K V Khanapara
Here are the answers with explanations:
(i) True. Every natural number is a whole number. The set of natural numbers is a subset of the set of whole numbers.
(ii) True. Every integer is a whole number. The set of integers contains the set of whole numbers.
(iii) False. Not every rational number is a whole number. Rational numbers also include fractions and terminating/repeating decimals.
(iv) True. Every irrational number is a real number. The set of irrational numbers is a subset of the set of real numbers.
(v) False. Not every real number is irrational. The set of real numbers contains both rational and irrational numbers.
(vi
Class9 number system
Rational numbers are numbers that can be represented as fractions p/q where p and q are integers and q is not equal to 0, such as 2/5 or 4/7. Irrational numbers are numbers that cannot be represented as fractions, such as √2 or √3, and their decimal representations are non-terminating and non-repeating. Real numbers include both rational and irrational numbers and can all be represented as unique points on a number line, with rational numbers having either terminating or non-terminating repeating decimals and irrational numbers having non-terminating, non-repeating decimals.
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This document reviews representations of different types of numbers on the number line. It discusses natural numbers, integers, rational numbers like terminating and repeating decimals, and irrational numbers like √2 that are non-terminating and non-repeating. Rational numbers can be represented as fractions p/q, while irrational numbers have decimal representations that do not terminate or repeat. The number line corresponds uniquely to real numbers, with infinitely many real numbers between any two real numbers.
Number System
The document provides an overview of number systems used by different civilizations and an introduction to basic number concepts:
- It discusses ancient number systems including the Egyptian base-12 and Babylonian base-60 systems, as well as modern systems like binary and decimal.
- Basic number types are defined such as integers, rational numbers, irrational numbers, and real numbers. Fractions and decimal expansions are also introduced.
- Famous mathematicians who contributed to the study and development of number systems throughout history are acknowledged.
number system school ppt ninth class
To download -https://clk.ink/MS2T
this will lead to a google drive link./
its a ppt based on the topic no. system.
it covers all the basics of ninth class cbse.
Number system
This document provides an overview of different types of real numbers:
- Rational numbers can be written as fractions p/q where p and q are integers. Their decimals are terminating or repeating.
- Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimals.
- Real numbers include all rational and irrational numbers and can be represented on the real number line. The document discusses properties and operations of real numbers.
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This document discusses different types of number systems. It begins by introducing natural numbers, which are counting numbers formed by repeated addition of 1. Whole numbers include all natural numbers and 0. Integers extend whole numbers infinitely in both the positive and negative directions. Rational numbers are numbers that can be written as fractions p/q where p and q are integers. Irrational numbers have non-repeating decimal expansions and cannot be written as fractions. Real numbers include all rational and irrational numbers and are represented on the number line. Methods for finding rational numbers between two given numbers and representing different types of numbers on the number line are also described.
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Real numbers include rational numbers like integers and fractions as well as irrational numbers like square roots and pi. Real numbers can be represented on a continuous number line and include both countable and uncountable infinite numbers. Real numbers have the properties of a field where they can be added, multiplied, and ordered on the number line in a way compatible with these operations. Rational numbers are numbers that can be represented as fractions of integers, and they include integers, whole numbers, and natural numbers. Irrational numbers cannot be represented as fractions.
Number system for class Nine(IX) by G R Ahmed TGT(Maths) at K V Khanapara
Here are the answers with explanations:
(i) True. Every natural number is a whole number. The set of natural numbers is a subset of the set of whole numbers.
(ii) True. Every integer is a whole number. The set of integers contains the set of whole numbers.
(iii) False. Not every rational number is a whole number. Rational numbers also include fractions and terminating/repeating decimals.
(iv) True. Every irrational number is a real number. The set of irrational numbers is a subset of the set of real numbers.
(v) False. Not every real number is irrational. The set of real numbers contains both rational and irrational numbers.
(vi
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Rational numbers are numbers that can be represented as fractions p/q where p and q are integers and q is not equal to 0, such as 2/5 or 4/7. Irrational numbers are numbers that cannot be represented as fractions, such as √2 or √3, and their decimal representations are non-terminating and non-repeating. Real numbers include both rational and irrational numbers and can all be represented as unique points on a number line, with rational numbers having either terminating or non-terminating repeating decimals and irrational numbers having non-terminating, non-repeating decimals.
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This document reviews representations of different types of numbers on the number line. It discusses natural numbers, integers, rational numbers like terminating and repeating decimals, and irrational numbers like √2 that are non-terminating and non-repeating. Rational numbers can be represented as fractions p/q, while irrational numbers have decimal representations that do not terminate or repeat. The number line corresponds uniquely to real numbers, with infinitely many real numbers between any two real numbers.
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The document provides an overview of number systems used by different civilizations and an introduction to basic number concepts:
- It discusses ancient number systems including the Egyptian base-12 and Babylonian base-60 systems, as well as modern systems like binary and decimal.
- Basic number types are defined such as integers, rational numbers, irrational numbers, and real numbers. Fractions and decimal expansions are also introduced.
- Famous mathematicians who contributed to the study and development of number systems throughout history are acknowledged.
number system school ppt ninth class
To download -https://clk.ink/MS2T
this will lead to a google drive link./
its a ppt based on the topic no. system.
it covers all the basics of ninth class cbse.
Number system
This document provides an overview of different types of real numbers:
- Rational numbers can be written as fractions p/q where p and q are integers. Their decimals are terminating or repeating.
- Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimals.
- Real numbers include all rational and irrational numbers and can be represented on the real number line. The document discusses properties and operations of real numbers.
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Whole numbers include the natural numbers (1, 2, 3, etc.) and zero. They can be represented on a number line and have important properties - zero is the smallest whole number, there are an infinite number of whole numbers, and each whole number has a unique successor and predecessor obtained by adding or subtracting 1.
Rational numbers ppt
Rational numbers are numbers that can be written as fractions p/q, where p and q are integers and q is not equal to 0. Rational numbers have important properties:
1) They are closed under addition and multiplication, meaning the sum or product of two rational numbers is also rational.
2) Operations like addition and multiplication are commutative and associative, following standard order of operations rules.
3) They follow the distributive property, where multiplying a number times the sum of two other numbers equals the sum of multiplying each number individually.
4) Each rational number has an additive inverse (its negative) and a multiplicative inverse (its reciprocal), such that adding/multiplying a number by its inverse results
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This is meant for age group 11 to 14 years.
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Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
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Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
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John scored 17 points (4x4 + 0x1 + -1x3 = 17)
Mary scored 20 points (4x5 = 20)
Adam scored 18 points (4x4 + -1x2 = 18)
Lisa scored 30 points (4x7 + 0x1 + -1x2 = 30)
Kim scored 31 points (4x7 + 4x1 = 31)
Jenny scored 32 points (4x8 = 32)
Zack scored 27 points (4x6 + 4x1 = 27)
Amy scored 25 points (4x5 + 4x1 = 25)
The students sorted from highest to lowest scores are:
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“Numbers do not feel. Do not bleed or weep or hope. They do not know bravery or sacrifice. Love and allegiance. At the very apex of callousness, you will find only ones and zeros.”
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Numebr system
- 1. NUMBER SYSTEM in our The NUMBERS play vital role life. Counting Numbers begin from 1 The smallest Number is 1 Next number, called Successor is obtained by adding 1 to the number However there is NO largest Number. Number 0 stands for
- 2. NATURAL NUMBERS The NATURAL NUMBERS begin from 1 1 is smallest NATURAL NUMBER There is NO largest NATURAL NUMBER NATURAL NUMBERS are INFINITE 1 2 3 4 5 6 7
- 3. WHOLE NUMBERS The WHOLE NUMBERS begin from 0 The smallest WHOLE NUMBER is 0 There is NO largest WHOLE NUMBER WHOLE NUMBERS are INFINITE 0 1 2 3
- 4. INTEGERS The INTEGERS are spread on BOTH sides of 0 The INTEGER 0 is neither POSITIVE nor NEGATIVE NEGATIVE numbers lie on the LEFT of 0 & POSITIVE numbers lie on the RIGHT of 0 For every + ve INTEGER x , there is a – ve INTEGER -x -3 -2 -1 0 1 2 3
- 5. RATIONAL NUMBERS A Number of the form p / q where p & q are INTEGERS and q ≠ 0, is called a RATIONAL NUMBER A RATIONAL NUMBER is POSITIVE OR NEGATIVE OR ZERO RATIONAL NUMBERS are EVERY WHERE DENSE ie in between any two given RATIONAL NUMBERS infinitely many RATIONAL NUMBERS can be placed
- 6. TERMINATING DECIMALS The Rational Numbers whose Denominator has ONLY 2 & 5 as its FACTORS , is always TERMINATING. Numerator divided by Denominator , gives Remainder Zero 7 / 50 is a Rational Number D = 50 50 = 2 x 5 x 5 Hence , 7 / 50 is Terminating
- 7. NON-TERMINATING REPEATING DECIMALS The Rational Numbers whose Denominator has FACTORS other than 2 & 5 , is always NONTERMINATING. Numerator divided by Denominator , gives Remainder other than Zero 1 / 3 has 3 as Denominator Numerator divided by Denominator gives Value as 0 . 33 3 . . . The repeating of 3 NEVER terminates
- 8. NON-TERMINATING NON REPEATING DECIMALS The Numbers in which Numerator divided by Denominator is NOT regular , are IRRATIONAL NUMBERS The values of π , √2 & √3 etc are IRRATIONAL NUMBERS π = 3.14…………… √2=1.414…………. √3 =1.732………….
- 9. IRRATIONAL NUMBERS The numbers which are NOT RATIONAL, are IRRATIONAL NUMBERS The NONTERMINATING NON REPEATING DECIMALS are called IRRATIONAL NUMBERS IRRATIONAL NUMBERS π = 3.14… √2=1.414… √3=1.732… The repeating of Decimal does NOT terminate
- 10. REAL NUMBERS The RATIONAL NUMBERS & IRRATIONAL NUMBERS together are called as REAL NUMBERS REAL NUMBER set is the LARGEST set