mathematics would be without irrational numbers? If the great Pythagorean hyppasus or any other mathematician would have not ever thought of such numbers? Before ‚understanding the development of irrational numbers ‚we should understand what these numbers originally are and who discovered them? In mathematics‚ an irrational number is any real number that cannot be expressed as a ratio a/b‚ where a and b are integers and b is non-zero. Irrational numbers are those real numbers that cannot be represented
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RATIONAL NUMBERS In mathematics‚ a rational number is any number that can be expressed as the quotient or fraction p/q of two integers‚ with the denominator q not equal to zero. Since q may be equal to 1‚ every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q it was thus named in 1895 byPeano after quoziente‚ Italian for "quotient". The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the
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In addition‚ stating that the square of rational numbers if being positive will be a square number. Book II explains how to basically represent in three simple methods. The methods are that if the square number is present whenever the squares of two rational numbers are being added; the addition of two new squares is the same thing as if adding two well-known squares; and if the rational number is given will be equal to their difference. The first and the third problem basically state that
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Counting Number : Is number we can use for counting things: 1‚ 2‚ 3‚ 4‚ 5‚ ... (and so on). Does not include zero; does not include negative numbers; does not include fraction (such as 6/7 or 9/7); does not include decimals (such as 0.87 or 1.9) Whole numbers : The numbers {0‚ 1‚ 2‚ 3‚ ...} There is no fractional or decimal part; and no negatives: 5‚ 49 and 980. Integers : Include the negative numbers AND the whole numbers. Example: {...‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3‚ ...} Rational numbers: It can
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REAL NUMBERS Q.1 Determine the prime factorization of the number 556920. (1 Mark) (Ans) 23 x 32 x 5 x 7 x 13 x 17 Explanation : Using the Prime factorization‚ we have 556920 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 13 x 17 = 23 x 32 x 5 x 7 x 13 x 17 Q.2 Use Euclid’s division algorithm to find the HCF of 210 and 55. (1 Mark) (Ans) 5 Explanation: 5 ‚ Given integers are 210 and 55 such that 210 > 55. Applying Euclid’s division leema to 210 and 55‚ we get 210 = 55 x 3 + 45 ………
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A rational number is a number that can be written as a ratio of two integers. The decimal of a rational number will either repeat or terminate. There is a way to tell in advance whether a rational number’s decimal representation will repeat or terminate. When trying to find a pattern in the relationship between rational numbers and their decimals‚ it is best to start with a list. A random list of rational numbers and their decimal values was made in order to find a pattern. The list included ½‚ 5/6
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------------------------------------------------- Real number In mathematics‚ a real number is a value that represents a quantity along a continuum‚ such as 5 (an integer)‚ 3/4 (a rational number that is not an integer)‚ 8.6 (a rational number expressed in decimal representation)‚ and π (3.1415926535...‚ an irrational number). As a subset of the real numbers‚ the integers‚ such as 5‚ express discrete rather than continuous quantities. Complex numbers include real numbers as a special case. Real numbers can be divided into rational numbers
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Real Numbers -Real Numbers are every number. -Therefore‚ any number that you can find on the number line. -Real Numbers have two categories‚ rational and irrational. Rational Numbers -Any number that can be expressed as a repeating or terminating decimal is classified as a rational number Examples of Rational Numbers 6 is a rational number because it can be expressed as 6.0 and therefore it is a terminating decimal. -7 ½ is a rational number because it can be expressed as -7.5 which is a
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mathematics‚ a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers‚ such as the integer −5 and the fraction 4/3‚ and all the irrational numbers such as √2 (1.41421356... the square root of two‚ an irrational algebraic number) and π (3.14159265...‚ a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line‚ where the points corresponding to integers are equally
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Question Number 1 Points: 5.00/5.00 Question Text What event marks the line between the Old English and Middle English periods? Your Answer B. the Norman invasion Question Number 2 Points: 0.00/5.00 Question Text What was the effect of the Norman conquest on the language of Britain? Your Answer . The upper class spoke French Question Number 3 Points: 0.00/5.00 Question Text Why is Beowulf an epic poem? Your Answer It is about a hero who represents cultural values.
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