geometric shapes‚ which lead to special numbers. The simplest example of these are square numbers‚ such as 1‚ 4‚ 9‚ 16‚ which can be represented by squares of side 1‚ 2‚ 3‚ and 4. Triangular numbers are defined as “the number of dots in an equilateral triangle uniformly filled with dots”. The sequence of triangular numbers are derived from all natural numbers and zero‚ if the following number is always added to the previous as shown below‚ a triangular number will always be the outcome: 1 = 1
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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
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IX Mathematics Chapter 1: Number Systems Chapter Notes Key Concepts 1. 2. 3. 4. 5. Numbers 1‚ 2‚ 3…….‚ which are used for counting are called Natural numbers and are denoted by N. 0 when included with the natural numbers form a new set of numbers called Whole number denoted by W -1‚-2‚-3……………..- are the negative of natural numbers. The negative of natural numbers‚ 0 and the natural number together constitutes integers denoted by Z. The numbers which can be represented in the form of p/q where
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to represent calculations. The Chinese system is also a base-10 system‚ but it has important differences in the way that the numbers are represented. The rod numbers were developed from counting boards‚ which came into use in the fourth century BC. A counting board had squares with rows and columns. Numbers were represented by little rods made from bamboo or ivory. A number was formed in a row with the units in the right-hand column‚ the tens in the next column‚ the hundreds in the next‚ and so on
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used Roman Numerals and noticed math. So they know how to use it. That is where numbers got their name. In Babylon and Egypt‚ the people first started using theoretical tools and numbering systems. The Egyptians used a decadic numbering system‚ which is based on the number 10 and still in use today. They also introduced characters used to describe the numbers 10 and 100‚ making it easier to describe larger numbers. Geometry started to receive great attention and served in surveying land‚ cities
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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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he number theory or number systems happens to be the back bone for CAT preparation. Number systems not only form the basis of most calculations and other systems in mathematics‚ but also it forms a major percentage of the CAT quantitative section. The reason for that is the ability of examiner to formulate tough conceptual questions and puzzles from this section. In number systems there are hundreds of concepts and variations‚ along with various logics attached to them‚ which makes this seemingly
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The Egyptian number system I choose to write about the Egyptian Number system because I am familiar with the base system they use. Therefore‚ it is easy for me to explain. In this essay I will briefly talk about the history of the Egyptian number system‚ indicate their base‚ symbols‚ whether their number system is positional or not and finally explain their number system by giving examples. The Egyptians had a writing system based on hieroglyphs from around 3000 BC. Hieroglyphs was found
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Complex Number System Arithmetic A complex number is an expression in the form: a + bi where a and b are real numbers. The symbol i is defined as √ 1. a is the real part of the complex number‚ and b is the complex part of the complex number. If a complex number has real part as a = 0‚ then it is called a pure imaginary number. All real numbers can be expressed as complex numbers with complex part b = 0. -5 + 2i 3i 10 real part –5; imaginary part 2 real part 0; imaginary part 3 real part 10; imaginary
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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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