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### Introduction

1. 1. Mathematics-1<br />Lecturer#1<br />
2. 2. Module Title: Mathematics 1 Module Type: Standard module Academic Year: 2010/11, Module Code: EM-0001D Module Occurrence: A, Module Credit: 20 Teaching Period: Semester 1 Level: Foundation   <br />
3. 3. Aims<br />Reinforcement of basic numeracy and algebraic manipulation.<br />A combination of lectures, seminars and tutorials is used to explain concepts and apply them through exercises<br />
4. 4. Study Hours<br />Lectures: 48.00<br />Directed Study: 138.00<br /> <br />Seminars/Tutorials: 32.00<br />Formal Exams: 2.00<br /> <br />Laboratory/Practical: 0.00<br />Other: 0.00<br />Total: 200 <br />
5. 5.
6. 6. Numbers<br />Number is a mathematical concept used to describe and access quantity.<br />
7. 7. The Beauty of Mathematics<br />Here is an interesting and lovely way to look at the beauty of mathematics, and of God, the sum of all wonders.<br />Wonderful World<br />
8. 8. 1 x 8 + 1 = 912 x 8 + 2 = 98123 x 8 + 3 = 9871234 x 8 + 4 = 987612345 x 8 + 5 = 98765123456 x 8 + 6 = 9876541234567 x 8 + 7 = 987654312345678 x 8 + 8 = 98765432123456789 x 8 + 9 = 987654321<br />
9. 9. 1 x 9 + 2 = 1112 x 9 + 3 = 111123 x 9 + 4 = 11111234 x 9 + 5 = 1111112345 x 9 + 6 = 111111123456 x 9 + 7 = 11111111234567 x 9 + 8 = 1111111112345678 x 9 + 9 = 111111111123456789 x 9 +10= 1111111111<br />
10. 10. 9 x 9 + 7 = 8898 x 9 + 6 = 888987 x 9 + 5 = 88889876 x 9 + 4 = 8888898765 x 9 + 3 = 888888987654 x 9 + 2 = 88888889876543 x 9 + 1 = 8888888898765432 x 9 + 0 = 888888888 <br />Brilliant, isn’t it?<br />
11. 11. And look at this symmetry:<br />1 x 1 = 111 x 11 = 121111 x 111 = 123211111 x 1111 = 123432111111 x 11111 = 123454321111111 x 111111 = 123456543211111111 x 1111111 = 123456765432111111111 x 11111111 = 123456787654321111111111 x 111111111 = 12345678987654321 <br />
12. 12. Number Representation<br />The number system that we use today has taken thousand of years to develop. <br />The Arabic system that we commonly use consists of exactly ten symbols:<br />0 1 2 3 4 5 6 7 8 9<br />Each symbol is called a digit. Our system involves counting in tens. This type of system is called denary system, and 10 is called the base of the system.<br />It is possible to use a number other than 10. For example, computer systems use base 2( the binary system)<br />Numbers are combined together, using the four arithmetic operations.<br />addition (+), subtraction (-), multiplication (×) and division (÷)<br />
13. 13. Powers<br />Repeated multiplication by the same number is known as raising to a power. For example 8×8×8×8×8 is written 85 (8 to the power 5) Check your calculator for xy.<br />
14. 14. Place value<br />Once a number contains more then one digits, the idea of place value is used to tell us its worth. In number 2850 and 285, the 8 stands for something different. In 285, 8 stands for 8 ‘tens’. In 2850, the 8 stands for 8 ‘hundreds’. The following table show the names given to the first seven places.<br />The number shown is 4087026, which is 4 million eighty-seven thousands and twenty-six.<br />
15. 15. Real Numbers<br />Real Numbers are any number on a number line. It is the combined set of the rational and irrational numbers.<br />
16. 16. Rational Numbers<br />Rational Numbers are numbers that can be expressed as a fraction or ratio of two integers.<br />Example: 3/5, 1/3, -4/3, -25<br />
17. 17. Irrational Numbers<br />Irrational Numbers are numbers that cannot be written as a ratio of two integers. The decimal extensions of irrational numbers never terminate and never repeat.<br />Example: – 3.45455455545555…..<br />
18. 18. Ratio/Quotient<br />A comparison of two numbers by division. The ratio of 2 to 3 can be stated as 2 out of 3, 2 to 3, 2:3 or 2/3.<br />
19. 19. Whole numbers<br />Whole numbers are 0 and all positive numbers such as 1, 2, 3, 4 ………<br />
20. 20. Integers<br />Any positive or negative whole numbers including zero. Integers are not decimal numbers are fractions. <br />. . .-3, -2, -1, 0, 1, 2, 3, …<br />
21. 21. The Real Number System<br />9/28/2010<br />jwaid<br />21<br />Real Numbers<br />Rational Numbers<br />Irrational Numbers<br />1/2<br />-2<br />2<br />3<br />3<br />2/3<br />0<br /><ul><li>5</li></ul> 2<br />3<br />4<br />15%<br />-0.7<br />1.456<br />
22. 22. The Real Number System<br />9/28/2010<br />jwaid<br />22<br />Real Numbers<br />Rational Numbers<br />Irrational Numbers<br />Integers<br />2<br />3<br />3<br />-2<br />1/2<br />2/3<br />0<br /><ul><li>5</li></ul> 2<br />3<br />4<br />15%<br />1.456<br />- 0.7<br />
23. 23. The Real Number System<br />9/28/2010<br />jwaid<br />23<br />Real Numbers<br />Rational Numbers<br />Irrational Numbers<br />Integers<br /> Whole <br />2<br />3<br />3<br />1/2<br />2/3<br />0<br /><ul><li>5</li></ul> 2<br />3<br />4<br />-2<br />15%<br />1.456<br />- 0.7<br />
24. 24. x<br />-5<br />-1<br />-4<br />-2<br />-3<br />1<br />5<br />2<br />3<br />4<br />0<br />Properties of Real Numbers <br />All of the numbers that you use in everyday life are real numbers.<br />Each real number corresponds to exactly one point on the number line, and<br />every point on the number line represents one real number.<br />
25. 25. Rational numbers can be expressed as a ratio , where a and b are<br />integers and b is not ____! <br />Properties of Real Numbers <br />Real numbers can be classified as either _______ or ________.<br />rational<br />irrational<br />zero<br />The decimal form of a rational number is either a terminating or repeating decimal.<br />Examples: ratio form decimal form <br />
26. 26. Properties of Real Numbers <br />Real numbers can be classified a either _______ or ________.<br />rational<br />irrational<br />A real number that is not rational is irrational.<br />repeats<br />The decimal form of an irrational number neither __________ nor ________.<br />terminates<br />Examples: <br />More Digits of PI?<br />Do you notice a pattern within this group of numbers?<br />They’re all PRIME numbers!<br />
27. 27. Example 1<br />Classify each number as being real, rational, irrational, integer, whole, and/or natural numbers. Pick all that apply.<br />
28. 28. For example, is a whole number, but , since it lies between 5 and 6, must be irrational.<br />2<br />3<br />6<br />0<br />10<br />9<br />4<br />5<br />8<br />7<br />1<br />x<br />Properties of Real Numbers <br />The square root of any whole number is either whole or irrational.<br />Common Misconception:<br />Do not assume that a number is irrational just because it is expressed using the <br />square root symbol.<br />Find its value first!<br />Study Tip:<br />KNOW and recognize (at least) these numbers,<br />
29. 29. Any<br /> ?<br />