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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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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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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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 as
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Quantum Numbers Quantum Numbers The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit‚ which was described by the n quantum number. Schrödinger’s model allowed the electron to occupy three-dimensional space. It therefore required three coordinates‚ or three quantum numbers‚ to describe the orbitals in which electrons can be found. The three coordinates that
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MATH 4 A. DIVISION of WHOLE NUMBERS B. DECIMALS a. PLACE VALUE of DECIMALS PLACE VALUE | Trillions | Billions | Millions | Thousands | Ones / Unit | Decimalpoint | .1 | .01 | .001 | HUNDRED | TEN | TRILLIONS | HUNDRED | TEN | BILLIONS | HUNDRED | TEN | MILLIONS | HUNDRED | TEN | THOUSANDS | HUNDREDS | TENS | ONES | | TENTHS | HUNDREDTHS | THOUSANDTHS | 5 | 8 | 9‚ | 6 | 1 | 2‚ | 7 | 4 | 5‚ | 6 | 1 | 8‚ | 3 | 2 | 5 | . | 1 | 6 | 2 | b. READING and WRITING DECIMALS
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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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Assignment Simple Superstitions: Number “thirteen” One of the pseudoscientific claim for the Number “thirteenth” is that people think it is just a superstition when some people believe in it and some people don’t. Everyone has their own opinion and belief in particular things. The Number “thirteenth” is most likely known for its unlucky date‚ unlucky number‚ and its unlucky self. The Number “thirteenth” has so much history to it‚ to why it’s unlucky. People believe the number thirteenth is unlucky‚ and
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Convert the decimal number 125 into binary. Use the division-by-two method shown in the following example. 125 /2 = 62 r=1 62 /2 = 31 r=0 31 /2 = 15 r=1 15 /2 = 7 r=1 7 /2 = 3 r=1 3 /2 = 1 r=1 1 /2 = 0 r=1 01111101 2.Convert your binary result back into decimal to prove your answer is correct. This is also shown in the following example. Weights = 128 64 32 16 8 4 2 1 Bits = 0 1 1 1 1 1 0 1 64 + 32 + 16 + 8 + 4 + 1 = 125 Task 2: Procedure 1.Convert the binary number 10101101 into decimal
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Digital Electronics‚ 2003 BINARY CODED DECIMAL: B.C.D. • ANOTHER METHOD TO REPRESENT DECIMAL NUMBERS • USEFUL BECAUSE MANY DIGITAL DEVICES PROCESS + DISPLAY NUMBERS IN TENS IN BCD EACH NUMBER IS DEFINED BY A BINARY CODE OF 4 BITS. *** 8 – 4 – 2 – 1 MOST COMMON CODE 8 – 4 – 2 – 1 CODE INDICATES THE WEIGHT OF EACH BIT 23 – 22 – 21 – 20 E.G. 934 = 1001 0011 0100 9 3 4 FOR EACH DIGIT A BINARY [NORMAL] CODE IS ALLOCATED. OHER REPRESENTATION FORMS ARE 2-4-2-1 AND EXCESS-3 Ovidiu Ghita Page
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