# Bahasa Inggris NUMBER

Penyusun Zulkifli Paldana Akbar

Teknik Konstruksi Sipil 1s2 sore
POLITEKNIK NEGERI JAKARTA 2010

definition
Number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word is used for both the abstract and the symbol. As well as for the word. In addition to their use in counting and measuring. Numeral are often used for labels (telephone number), for ordering (serial number), and for codes (e.g ISBN). In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.

Complex numbers . Integers d.The Types of Number a. Natural numbers b. Whole numbers c. Real number f. Rational numbers e.

3. … ) or.2.2. non-negative numbers (0.a. … . Natural numbers is an ordinary counting numbers or is a number that occurs in commonly and obviously in nature.5. Natural numbers consist of positive integers or counting numbers (1. …).1. in some cases.3. and ordering (“that is the 4th largest planet”).4. Natural numbers have two main purposes : counting (“there are 2 dogs”).2. Example : 1.3.

. 1. . 0.3.2. -3. .. 1.) • the positive integers (1. -2.) • all integers (. Whole numbers is an integer equal to or greater than zero. Example : 0... 2... Various authors use it in one of the following senses: • the nonnegative integers (0.b. … The term whole number does not have a consistent definition. 2. 3... .) . 3.1. 2.4.. -1. 3. The whole numbers exactly does not have a consistent definition.

When two integers are added.-25.5. integers can not have decimal place. However. but 6 divided by 4 equals 1.c.148 are all integers. or multiplied. substracted.0. when one integer is divided into another. Decimal number may either be rounded or truncated to produce an integer result. which contains a fraction. Therefore. unlike floating point numbers. which is an integer. the result may be an integer or a fraction. Integers is whole number (not a fraction) that can be positive. and 5. For example : 6 divided by 3 equals 2. the numbers 10. or zero. . negative. the result is also an integer.

where b is not zero. A rational number is a number which can be expressed as a ratio of two integers. excluding zero as a denominator. Rational numbers is a number that can be written as a simple fraction or A number capable of being expressed as an integer or a quotient of integers. Noninteger rational numbers (commonly called fractions) are usually written as a/b. .d. A rational number is a number that can be in the form p/q where p and q are integers and q is not equal to zero.

. Pi and the square root of 2 (2) are irrational numbers.e. it is a number which cannot be expressed as a fraction m/n. An example of an irrational number is π ≈ 3. an irrational number would have an infinite number of digits to the right of the decimal point. irrational numbers is any real number that is not a rational number. If written in decimal notation.. where m and n nonzero. without repetition.141592653589793. Specifically..

5. 3/7 . -12. The numbers 2. and irrational numbers.. Real numbers can be divided into rational numbers. such as 42 and −23/129. such as pi and the square root of two. 8. 3/4 (a rational number that is not an integer). a rational or irrational number. such as 5 (whole numbers that express discrete rather than continuous quantities) and complex numbers (mathematical constructs that include real numbers as a special case). Real numbers are commonly opposed both to integers.. and pi (π) are all real numbers. and pi (3. is a value that represents a quantity along acontinum. an irrational number)..e. .6 (a rational number expressed in decimal representation).1415926535. Real number is a number that can be written as a terminating or non-terminating decimal. such as 5 (an integer).

where the digits continue indefinitely. etc… Positive or negative.. They are called "Real Numbers" because they are not Imaginary Numbers. large or small.. -0.4871773339 . whole numbers or decimal numbers are all Real Numbers. 15. ..A real number can be given by an infinite decimal representation. The real numbers are sometimes thought of as points on an infinitely long number line.1. 3/4. such as 2. such as 1.82. The type of number we normally use.

during his attempts to find solutions to cubic equations. even when the final solutions are real numbers. where any polynomial equation has a root. and i is the standard imaginary unit with the property i 2 = −1. Complex numbers were first conceived and defined by the Italian mathematician Gerolamo Cardano. This ultimately led to the fundamental theorem of algebra. which shows that with complex numbers. Complex numbers thus form an algebraically closed field. who called them "fictitious".[2] The solution of a general cubic equation in radicals (without trigonometric functions) may require intermediate calculations containing the square roots of negative numbers. but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication.f. a situation known as casus irreducibilis.[1] The complex numbers contain the ordinary real numbers. It can be written in the form a + bi. where a and b are real numbers. . a solution exists to every polynomial equation of degree one or higher. A complex number is a number consisting of a real and imaginary part.

[3] A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton. multiplication. and division of complex numbers were developed by the Italian mathematician Rafael Bombelli. and complex Lie algebra.The rules for addition. quantum physics. the name usually reflects that fact. Complex numbers are used in a number of fields. complex matrix. on which . Complex numbers are plotted on the complex plane. applied mathematics. electromagnetism. subtraction. Examples are complex analysis. complex polynomial. When the underlying field of numbers for a mathematical construct is the field of complex numbers. who extended this abstraction to the theory of quaternions. and chaos theory. including: engineering.

n where a and b are integers and b is not zero The limit of a convergent sequence of rational numbers a + bi where a and b are real numbers and i is the square root of −1 . 3. −1. .. 4 . 1... 5 .. n 1 . 4. −2. 5. 3.. . . −4. . 4.. 1. 0.Number System Natural Integers Positive integer rational Real complex (0). 3 . . a⁄ b 2 . −3. 5. . 7.. 2. . −5.. 6.. 2. n −n.

True or False: A number is either a rational or an irrational.• Here are some typical number-type questions (assuming that you haven't yet learned about imaginaries and complexes): Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved True or False: An integer is a rational number. but 2/3 is not! So this is false. a number is either non-terminating and non-repeating (so it's an irrational) or not (so it's a rational). • Not necessarily. • True! In decimal form. there is no overlap between these two number types! . • Since any integer can be formatted as a fraction by putting it over 1. True or False: A rational is an integer. 4/1 is an integer. but not both. then this is true.

14159265358979323846264338327950288419716939937510. Since this fraction does not reduce to a whole number. . real . some numbers may be of more than one type. however. • 0. but it isn't pi! This is a rounded decimal approximation. this is actually a rational. though this may be more decimal places than you customarily use. then it's not an integer or a natural. unlike pi which is irrational! The answer is: rational.. real • 3. so it can be written as a fraction: 45/ 9 100 = /20. You probably recognize this as being pi. so pi is an irrational.14159 Don't let this fool you! Yes. and. And everything (that you know about so far) is a real. And everything is a real.45 This is a terminating decimal. you often use something like this as an approximation of pi. since this approximation terminates. real • 3. so the answer is: irrational. so the answer is: rational.Classify according to number type. is that the decimal does not repeat. The point.

because it's a square root. The answer is: integer (possibly). The answer is: natural. this may also be counted as a rational. It's also a real. rational. but notice that this square root simplifies: –sqrt(81) = – 9. but notice that it reduces to –3. That means it is also a whole number and an integer. real • –sqrt(81) Your first impulse may be to say that this is irrational. which is the same as the previous problem. so this may also count as an integer. Depending on the text and teacher (there is some inconsistency).• 10 Obviously. real • – 9/3 This is a fraction. rational. And of course it's also a real. whole. this is a counting number. so it's a rational. rational (possibly). real • 1 2/3 This can also be written as 5/3. The answer is: rational. so the answer is: rational. real • 5/3 This is a fraction. real . which technically-speaking it is. which is just an integer. The answer is: integer. integer.

you should know that the term refers to the counting numbers. if your teacher talks about "integers". It's more important to know what the terms mean when you hear them. you really won't need to be terribly familiar with this hierarchy. and zero. .Except for the section where you have to classify numbers according to type. For instance. their negatives.

_____. Natural numbers : • 5+5=… • Fill in the missing number : ___ ten and 7 ones = 17 • Between 9. 11 Ans : 10 (for all question) b. Whole numbers : • Write the number below in words Eg : 4 159 Ans : Four thousand one-hundred and fifty nine • Write each in expanded form Eg : 517 249 ans : 500 000 + 10 000 + 7 000 + 200 + 40 + 9 .The exercise a.

3 c. Eg : 2 719 ans : 2(thousands). 7(hundreds).-3 d.8? a. 13 b. 87 • What is 5 .• Give the place value of each digit in the following numbers. 9(ones) c.87 ans :c. -13 ans :c.97 c. positive • What is the magnitude of 87? a. Integers • Is 8 positive or negative? ans : yes. -3 .100 b. 1(tens).

|−3|=3 .2 a rational number? • Is -5. which is −(−3). Rational numbers • Is 3. −(−3)=3. This part says that the absolute value of 8 is 8 itself • |-3| The number enclosed within absolute value bars is a negative number so the second part of the definition applies. Real numbers • |8| The number enclosed within the absolute value bars is a nonnegative number so the first part of the definition applies.d. This part says that the absolute value of −3 is the opposite of −3. By the double-negative property.321671 a rational number? ans : yes (for all question) e.

Complex numbers • Simplify ί 9 ί 9 = ί 2 ί 2 ί 2 ί 2 ί = (-1)(-1)(-1)(-1) ί = ί • Find √-49 √-49 = √-1 √49 = ±7 ί .f.

may be understood and we all know about the various numbers and usefulness. prime. fractional. Thus the classification number that can be explained. many explanations. integral. decimal and more.ending number was classified according to the utility's own numbers. turned out to not only learn the number adding and subtracting or dividing and multiplying numbers only. each number has an explanation in accordance with the part. . and from which all numbers can be formed into integer.

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