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# Number system

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### Number system

1. 1. A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbolfor three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
2. 2.  The most commonly used system of numerals is known as Arabic numerals or HinduTwo Indian mathematicians are credited with developing them. Aryabhata of Kusumapura develope d the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero.[1] The numeral system and the zero concept, developed by the Hindus in India slowly spread to other surrounding countries due to their commercial and military activities with India. The Arabs adopted it and modified them. Even today, the Arabs called the numerals they use Rakam Al-Hind or the Hindu numeral system. The Arabs translated Hindu texts on numerology and spread it to the western world due to their trade links with them.
3. 3.  positional system, also known as place-value notation. Again working in base 10, ten different digits 0, ..., 9 are used and the position of a digit is used to signify the power of ten that the digit is to be multiplied with, as in 304 = 3×100 + 0×10 + 4×1. Note that zero, which is not needed in the other systems, is of crucial importance here, in order to be able to "skip" a power. The Hindu-Arabic numeral system, which originated in India and is now used throughout the world, is a positional base 10 system. Arithmetic is much easier in positional systems than in the earlier additive ones; furthermore, additive systems need a large number of different symbols for the different powers of 10; a positional system needs only ten different symbols (assuming that it uses base 10). The numerals used when writing numbers with digits or symbols can be divided into two types that might be called the arithmetic numerals 0,1,2,3,4,5,6,7,8,9 and the geometricnumerals 1,10,100,1000,10000... respectively. The sign-value systems use only the geometric numerals and the positional systems use only the arithmetic numerals. The sign-value system does not need arithmetic numerals because they are made by repetition (except for the Ionic system), and the positional system does not need geometric numerals because they are made by position. However, the spoken language uses both arithmetic and geometric numerals.
4. 4.  p/q where p and q are integers and q ! 0 are known as rational numbers. The collection of numbers of the form p/q , where q > 0 is denoted by Q. Rational numbers include natural numbers, whole numbers, integers and all negative and positive fractions. Here we can visualize how the girl collected all the rational numbers in a bag. Rational numbers can also be represented on the number line and here we can see a picture of a girl walking on the number line. To express rational numbers appropriately on the number line, divide each unit length into as many number of equal parts as the denominator of the rational number and then mark the given number on the number line.
5. 5. The process of visualization ofrepresentation of numbers on thenumber line through a magnifyingglass is known as the process ofsuccessive magnification.
6. 6. This module is from ElementaryAlgebra by Denny Burzynski andWade Ellis, Jr. The symbols,notations, and properties ofnumbers that form the basis ofalgebra, as well as exponents andthe rules of exponents, areintroduced in this chapter. Eachproperty of real numbers and therules of exponents are expressedboth symbolically and literally.Literal explanations are includedbecause symbolic explanationsalone may be difficult for a studentto interpret. Objectives of thismodule: understand exponentialnotation, be able to readexponential notation, understandhow to use exponential notationwith the order of operations.
7. 7. In elementaryalgebra, rootrationalisation is aprocess bywhich surds inthe denominator ofan irrational fraction areeliminated.These surds maybe monomials or binomials involving squareroots, in simpleexamples. There arewide extensions to thetechnique.
8. 8. It is difficult to dealwith the expressionhaving square rootin the denominator.This raises a need ofremoving squareroot from thedenominator. It canbe done byrationlising thedenominator.
9. 9.  1. Numbers 1, 2, 3…….∞, which are used for counting are called Natural  16. Real numbers satisfy the commutative, associate and distributive numbers and are denoted by N.  law of addition and multiplication. 2. 0 when included with the natural numbers form a new set of  17. Commutative law of addition: If a and b are two real numbers then, numbers  a+b=b+a called Whole number denoted by W  18. Commutative law of multiplication: If a and b are two real 3. -1,-2,-3……………..-∞ are the negative of natural numbers.  numbers then, a. b = b. a 4. The negative of natural numbers, 0 and the natural number together  19. Associative law of addition: If a, b and c are real numbers then, constitutes integers denoted by Z.  a + (b + c) = (a + b) + c 5. The numbers which can be represented in the form of p/q where  20. Associative law of multiplication: If a, b and c are real numbers q 0 ≠ and p and q are integers are called Rational numbers. Rational  then, a. (b. c) = (a. b). c numbers are denoted by Q. If p and q are co prime then the rational  21. Distributive of multiplication with respect to addition: If a, b and number is in its simplest form.  c are real numbers then, a. (b+ c) = a. b + a. c 6. Irrational numbers are the numbers which are non-terminating and  22. Removing the radical sign from the denominator is called non-repeating.  rationalisation of denominator. 7. Rational and irrational numbers together constitute Real numbers  23. The multiplication factor used for rationalizing the denominator is and it is denoted by R.  called the rationalizing factor. 8. Equivalent rational numbers (or fractions) have same (equal)  24. The exponent is the number of times the base is multiplied by values when written in the simplest form. itself. 9. Terminating fractions are the fractions which leaves remainder 0 on  25. In the exponential representation division.  m 10. Recurring fractions are the fractions which never leave a remainder  a , a is called the base and m is 0 on division.  called the exponent or power. 11. There are infinitely many rational numbers between any two  26. If a number is to the left of the number on the number line, it is less rational  than the other number. If it is to the right, then it is greater than the numbers.  number. 12. If Prime factors of the denominator are 2 or 5 or both only. Then the  27. There is one to one correspondence between the set of real number is terminating else repeating/recurring.  numbers and the set of point on the number line. 13. Two numbers p & q are said to be co-prime if, numbers p & q have no common factors other than 1.
10. 10. The origins and history of number system.We call them ArabicNumerals, but ournumbers actually findtheir origins in the historyof the Hindus of India.They have changed greatlyover the centuries, passingfirst to the Arabs of theMiddle East and finally toEurope in the MiddleAges, and are now themost commonly usednumbers throughout theworld.
11. 11. ThanksName - Prajjwal KushwahaClass - flyers-1-bRoll no -28Special thanks to Mr.pradeep Kumar lodha