Introduction Combined Number And Dp

Module Title: Mathematics 1 Module Type: Standard module Academic Year: 2009/10, Module Code: EM-0001D Module Occurrence: A, Module Credit : 20 Teaching Period: Semester 1 Level: Foundation

Reinforcement of basic numeracy and algebraic manipulation. Learning Teaching & Assessment Strategy: A combination of lectures, seminars and tutorials is used to explain concepts and apply them through exercises

Study Hours Lectures: 36.00 Directed Study: 138.00 Seminars/Tutorials: 24.00 Formal Exams: 2.00 Laboratory/Practical: 0.00 Other: 0.00 Total: 200

1 Assessment Type Duration (hours) Percentage Classroom test - 25% Description 2 classroom tests each lasting 1 hour 2 Assessment Type Duration (hours) Percentage Examination - open book or seen paper 2 50% Description Examination 3 Assessment Type Duration (hours) Percentage Coursework - 25% Description 2 assignments consisting of Maths questions taking approx 2 hours to answer per assignment 900 Assessment Type Duration (hours) Percentage Examination - open book or seen paper 2 100% Description Supplementary examination

Number is a mathematical concept used to describe and access quantity.

Here is an interesting and lovely way to look at the beauty of mathematics, and of God, the sum of all wonders. The Beauty of Mathematics Wonderful World

1 x 8 + 1 = 9 12 x 8 + 2 = 9 8 123 x 8 + 3 = 9 8 7 1234 x 8 + 4 = 9 8 7 6 12345 x 8 + 5 = 9 8 7 6 5 123456 x 8 + 6 = 9 8 7 6 5 4 1234567 x 8 + 7 = 9 8 7 6 5 4 3 12345678 x 8 + 8 = 9 8 7 6 5 4 3 2 123456789 x 8 + 9 = 9 8 7 6 5 4 3 2 1

9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888 Brilliant, isn’t it?

1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 +10= 1111111111

1 x 1 = 1 11 x 11 = 1 2 1 111 x 111 = 1 2 3 2 1 1111 x 1111 = 1 2 3 4 3 2 1 11111 x 11111 = 1 2 3 4 5 4 3 2 1 111111 x 111111 = 1 2 3 4 5 6 5 4 3 2 1 1111111 x 1111111 = 1 2 3 4 5 6 7 6 5 4 3 2 1 11111111 x 11111111 = 123456787654321 111111111 x 111111111 = 12345678987654321 And look at this symmetry:

The number system that we use today has taken thousand of years to develop. The Arabic system that we commonly use consists of exactly ten symbols: 0 1 2 3 4 5 6 7 8 9 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. It is possible to use a number other than 10. For example, computer systems use base 2( the binary system) Numbers are combined together, using the four arithmetic operations. addition (+), subtraction (-), multiplication (×) and division (÷)

Repeated multiplication by the same number is known as raising to a power. For example 8×8×8×8×8 is written 8 5 (8 to the power 5) Check your calculator for x y .

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. The number shown is 4087026, which is 4 million eighty-seven thousands and twenty-six. Millions Hundreds thousands Ten thousands Thousands Hundreds Tens units 4 0 8 7 0 2 6

The Arabic numbering system uses ten symbols and is a base ten numbering system. In any numbering system the base is raised to consecutive powers to determine positional (place) values. 10 3 10 2 10 1 10 0 base powers 1000 100 10 1 place values 2 3 1 2 8 5 2 8 5 0

Real Numbers Real numbers consist of all the rational and irrational numbers. The real number system has many subsets: Natural Numbers Whole Numbers Integers

Natural Numbers Natural numbers are the set of counting numbers. {1, 2, 3,…}

Whole Numbers Whole numbers are the set of numbers that include 0 plus the set of natural numbers. {0, 1, 2, 3, 4, 5,…}

Integers Integers are the set of whole numbers and their opposites. {…,-3, -2, -1, 0, 1, 2, 3,…}

Rational Numbers Rational numbers are any numbers that can be expressed in the form of , where a and b are integers, and b ≠ 0 . Rational Numbers are numbers that can be expressed as a fraction or ratio of two integers They can always be expressed by using terminating decimals or repeating decimals.

Terminating Decimals Terminating decimals are decimals that contain a finite number of digits. Examples: 36.8 0.125 4.5

Repeating Decimals Repeating decimals are decimals that contain a infinite number of digits. Examples: 0.333… 7.689689… FYI…The line above the decimals indicate that number repeats.

Irrational Numbers Irrational numbers are any numbers that cannot be expressed as . They are expressed as non-terminating, non-repeating decimals ; decimals that go on forever without repeating a pattern. Examples of irrational numbers: 0.34334333433334… 45.86745893… (pi)

Other Vocabulary Associated with the Real Number System … (ellipsis)—continues without end { } (set)—a collection of objects or numbers. Sets are notated by using braces { }. Finite—having bounds; limited Infinite—having no boundaries or limits Venn diagram—a diagram consisting of circles or squares to show relationships of a set of data.

Example Classify all the following numbers as natural , whole , integer , rational , or irrational . List all that apply. 117 0 -12.64039… -½ 6.36 -3

To show how these number are classified, use the Venn diagram. Place the number where it belongs on the Venn diagram. Rational Numbers Integers Whole Numbers Natural Numbers Irrational Numbers -12.64039… 117 0 6.36 -3

Solution Now that all the numbers are placed where they belong in the Venn diagram, you can classify each number: 117 is a natural number, a whole number, an integer, and a rational number. is a rational number. 0 is a whole number, an integer, and a rational number. -12.64039… is an irrational number. -3 is an integer and a rational number. 6.36 is a rational number. is an irrational number. is a rational number.

10/05/10 jwaid Real Numbers Rational Numbers Irrational Numbers 3 1/2 -2 15% 2/3 1.456 -0.7 0  3 2   5 2 3  4

10/05/10 jwaid Real Numbers Rational Numbers Irrational Numbers 3 1/2 -2 15% 2/3 1.456 - 0.7 0  3 2   5 2 3  4 Integers

10/05/10 jwaid Real Numbers Rational Numbers Irrational Numbers 3 1/2 -2 15% 2/3 1.456 - 0.7 0  3 2   5 2 3  4 Integers Whole

All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and every point on the number line represents one real number. x 0 1 2 3 4 5 -5 -4 -2 -1 -3

Real numbers can be classified as either _______ or ________. rational irrational The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form zero Rational numbers can be expressed as a ratio , where a and b are integers and b is not ____!

Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Do you notice a pattern within this group of numbers? They’re all PRIME numbers!

Example 1 Classify each number as being real, rational, irrational, integer, whole, and/or natural numbers. Pick all that apply.

Decimal places (d.p.) refer to the digits to right of the decimal point. For example ‘23. 845 ’ have 3 decimal places. The numbers we get from a computation often contains worthless digits that must be thrown away. Whenever we do this we must round our answer to the required decimal places.

Rule 1 If the first digit to be discarded is greater than 5, or a 5 followed by a non zero in any of the decimal placed to the right, then round up by the last digit retained. Number Rounded to Three Decimal Places 4.3654 4.365 4.3656 4.366 4.365501 4.366 1.764999 1.765 1.927499 1.927

Rule 2 If the first digit to be discarded is less than 5, round down by the last digit retained. Write -6.0439 to 2 d.p. Here 3 is first discarded digit and 4 is the last retained digit. Since 3<5 so we round down and hence result will be -6.04.

Rule 3 (Important) If the first digit to be discarded is equal to 5, always round to the nearest even number. Numbers Rounded to 2 d.p. 4.365 4.36 4.355 4.36 7.76500 7.76 7.75500 7.76

Do not Forget to… When you were asked to write a number to for example to 3 d.p., consider the first 4 d.p. places during the computation and write the end result to 3 decimal places.

For example, here is a series of addition and result is required to 2.d.p

Introduction Combined Number And Dp

More Related Content

What's hot

Viewers also liked

Similar to Introduction Combined Number And Dp

More from Awais Khan

Introduction Combined Number And Dp