GROUP 1FANY RIZKI S.GRACE DANA AYORIHARUN ALRASYID F.RAHMAT SYAIFULLAHRYAN ADRIADI N.YUSUF AGUNG MAULANA

1 CIVIL 2 MORNING PROGRAMSTATE POLYTECHNIC OF JAKARTA

TYPES OF NUMBER

Different types of numbers are used in many cases.

NUMBER SYSTEM

The most familiar numbers are the natural numbers or counting numbers: one, two, three, and so on. Traditionally, the sequence of natural numbers started with 1 (0 was not even considered a number for the Ancient Greeks.) However, in the 19th century, set theorists and other mathematicians started including 0 (cardinality of the empty set, i.e. 0 elements, where 0 is thus the smallest cardinal number) in the set of natural numbers.[citation needed] Today, different mathematicians use the term to describe both sets, including zero or not.

The negative of a positive integer is defined as a number that produces zero when it is added to the corresponding positive integer.Negative numbers are usually written with a negative sign (a minus sign).Example : the negative of 7 is written −7, and 7 + (−7) = 0. When the set of negative numbers is combined with the set of natural numbers (which includes zero), the result is defined as the set of integer numbers, also called integers

A rational number is a number that can be expressed as a simple fraction with an integer numerator and a non-zero natural number denominator. Example :•1, 5 is rational because it can be writen as the ratio 3/2•7 is rational because it can be writen as the ratio 7/1•0,317 is rational because it can be writen as the ratio 317/100

Some number cannot be written as a ratio of two integers, they are called Irrational Numbers, because it cannot be written as a ratio (or fraction).Example :•π = 3,1415926535897932384626433832795 (and more…)•e = 2,7182818284590452353602874713527…•√ *ex √3 = 1,7320508075688772935274463415059…

The real numbers include all of the measuring numbers. This includes (but is not limited to) positive and negatives, integers and rational numbers, square roots, cube roots, π (pi), etc.R = Q Q’

COMPLEX NUMBERAre numbers built up from a real part and an imaginary part. The complex numbers consists of all numbers of the form: a + bi

here a and b are real numbers, and i is a mathemathical symbol which is called imaginary unit. (ex: 3+2i)C = {a+bi l a, b € R and I = √(-1)}

Precent means per hundred. 10 percent is just anotjer way of saying “ten out of a hundred,” or ten hundredths.

To convert a fraction to a precentage. Divide the numerator by the denominator. Yhen move the decimal point two places to the right (which is the same as multiplying by 100) and add a percent sign.

Example :•Given the fraction 5/8 what is the percentage ?

5/8 = 0,625 and than multiplying by 100

0,625x100 = 62,5 % and add a percent sign.•Change a percentage to a fraction, divide it by 100 and reduce the fraction or move the decimal point to the right until you have only integers :

10% = 10/100 = 1/10

62,5% = 62,5/100 = 625/1000

625/1000 = 125/200 = 25/40 = 5/8

Is a positive integer (p>1) that has no positive integer divisors other than 1 and itself.Example :•the only divisors of 13 are 1 and 13, making 13 a prime number (2, 3, 5, and 37 are the others examples of prime numbers)•24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24 (corresponding to the factorization), making 24 not a prime number.

Prime number are therefore numbers that cannot be factored.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.

PROPER FRACTIONis just a fraction where the numerator (the top number) is less than the denominator (the bottom number), like ½ (one-half), ¼ (one-quarter), ¾ (three-fourths), etc.

INPROPER FRACTIONis a fraction where the top number is bigger than the buttom number, like 7/4 (seven-fourths), etc.

MIXED FRACTIONa whole number and proper fraction together, like1¼, 2½, 3¾, etc. but for everyday use people understand mixed fractions better, like it is easier to say “I ate 2¼ sausages”, than “I ate 9/4 sausages”

is a fraction where the denominator is a power of ten.Decimal fractions are commonly expressed using decimal notation in which the implied denominator is determined by the number of digits to the right of a decimal separator, the appearance of which (e.g., a period, a raised period (•), a comma) depends on the locale. Thus for 0.75 the numerator is 75 and the implied denominator is 10 to the second power, viz. 100, because there are two digits to the right of the decimal separator. In decimal numbers greater than 1 (such as 3.75), the fractional part of the number is expressed by the digits to the right of the decimal (with a value of 0.75 in this case). 3.75 can be written either as an improper fraction, 375/100, or as a mixed number, .Decimal fractions can also be expressed using scientific notation with negative exponents, such as 6.023×10−7, which represents 0.0000006023. The 10−7 represents a denominator of 107. Dividing by 107 moves the decimal point 7 steps to the left.

BASIC OPERATION IN MATHEMATICS

Adding two (or more) numbers means to find their sum. The symbol used for addition is ‘+’Example : 5 + 10 = 15

five plus ten is equal to fifteenPROPERTY OF ADDITION•Commutative, forwards addition is the same as backwards addition. a+b = b+a [ex : 3+7 = 7+3 = 10]•Associative, addition of a list of numbers is the same regardless of which are added together first. a+(b+c) = (a+b)+c [ex: 1+(2+3) = (1+2)+3 = 6]

Substracting one number from another number is to find the difference between them. The symbol used for substraction is ‘–’Example :17 - 8 = 9

seventeen take away eight is equal to nine (17 minus 8 is 9)•Substraction is not in general commutative :

a – b ≠ 0 a - b ≠ b - aExample : [2 – 3 = -1] ≠ [3 – 2 = 1]

•Nor is it in general associativea – (b – c) ≠ (a – b) – cExample : [6 – (2 – 1)] ≠ [(6 – 2) – 1]

Multiplication means times (or repeated addition). The symbol used for multiplication is ‘x’. A product is the result of the multiplication of two (or more) numbers.Example : 7 x 2 = 14

seven times two is equal to fourteenProperty of Multiplication•Commutative

a x b = b x a[ex : 2 x 3 = 3 x 2 = 6]

•Associativea x (b x c) = (a x b) x c[ex: 3 x (4 x 5) = (3 x 4) x 5 = 60]

•Distributivea x (b + c) = (a x b) + (a x c)[ex : 2 x (3 + 4) = (2 x 3) + (2 x 4) = 14]

Division ‘undoes’ multiplication and involves a number called the dividend being ‘divided’ by another number called the divisiour. The symbol used for division is ‘÷’. A quotient is the result of division.Celarly, 9 x 8 = 72

72 ÷ 9 = 8 and 72 ÷ 8 = 9

Example :

Calculate 692 ÷ 4 !

Solution :

173 Quotient

Divisor 4 692 Dividend

4 -

29

28 -

12

12-

0 RemainderNote:•As division is the invers of multiplication, start by dividing 4 into the column furthest to the left.•6 ÷ 4 = 1 and 2 is the remainder•Clearly, the remainder 2 is 200 (i.e. 20 tens); and we can carry this into the tens column to make 29.•Now, 29 ÷ 4 = 7 with a remainder of 1. Clearly, the remainder of 1 is 10 (i.e. 10 uits) and we can carry this into the units column to make 12.•Finally, 12 ÷ 4 = 3

1. 4 – 2 ( … ) 2 – 4, the symbol of brackets is …2. 1 ¾, we read it …