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ASAS MENGENAL NOMBORPKP3183PISMP2015SISTEM PERNOMBORAN PURBASISTEM MESIRSISTEM BABYLONSISTEM MAYANSISTEM ROMANSISTEM NOMBOR MESIR?Angka Mesir purba ialah sejenis sistem angka yang telah digunakan di Mesir purba sehingga awal alaf pertama masihi. satu sistem angka perpuluhan (asas 10), sering dibundarkan kepada nilai yang lebih tinggi, ditulis dalam huruf Hieroglif tidak mempunyai nombor sifarSISTEM NOMBOR MESIRSetiap urutan magnitud (sa, puluh, ratus, ribu dan seterusnya) memiliki tanda khusus. Simbol Hieroglif diguna ada seperti dlm lampiran 1

Lampiran 1

SISTEM NOMBOR MESIR

SISTEM NOMBOR MESIRGandaan nilai-nilai boleh diungkapkan dengan mengulang simbol-simbol berdasarkan nilai yang dikehendaki. Contohnya, satu ukiran batu dari Karnak menunjukkan nombor 4622 seperti berikut.cth no mesir 4622.docxSISTEM BABYLON

Babylonian numeration system developed between 3000 and 2000 BCE.uses only two numerals or symbols, one and ten to represent numbers as follows:

SISTEM BABYLONExample:

two ones are shown on the right showed that Babylonians system used place value in their system.

Example of babylonian number45 is written as shown:

For numbers up to 59, the system was simply an additive system.

SISTEM BABYLONFor number bigger than 59, the babylonian used a place value system with a base of 60

62 is written as shown:

We can see the use of a big space to separate the place value.

SISTEM BABYLON62 =

Example:4871 could be represented as follow: 3600 + 1260 + 11 = 4871

Exercises:Write the following numbers using Babylonian numeration system:37743614SISTEM MAYANMayan numeration system evolved around A.D. 300.It used vertical place-value systemIt introduced a symbol for zero

SISTEM MAYANIt uses 3 basic numerals to represent any possible number: a dot for one, a horizontal bar for 5, and a conch shell for zero as follows:

Example:3 symbols above have been used to represent the numbers from 0 through 19 as shown below:

SISTEM MAYANFor number bigger than 19 is written in a vertical position so that it becomes a vertical place value system.Mayan numeration system was base 20 and their place values were 1, 20,18x20, 18x202, ...

SISTEM MAYANUsing the base 20, 1, 20, 202,203 20 = 1x20 + 0

100 = 5 x 20 + 0

SISTEM MAYAN2007 =5 x18x + 2 x 20 + 7 x 1

Exercises What is the value of this Mayan number?

Answer The number is: 14 + 7 20 + 1 202 + 3 20 3 + 0 20 4 + 15 20 5 + 5 20 6 = 368024554

SISTEM ROMANSistem Roman numeration system evolved around 500 BCE.it uses special symbols to represent numbers, the basic Roman numerals used are as follow:

SISTEM ROMANAll Roman numerals are found by combining these basic numerals using grouping, additivity, subtractive principle and multiplicative principle.Examples: 1) 154 =CLIIII in Roman numerals

2) 1492 =??????? in Roman numerals

3) 3495 =??????? in Roman numerals

Subtractive Principle 4) 4 = ??????? in Roman numerals 5) 9 = ??????? in Roman numerals 6) 40 = ????? in Roman numerals 7) 90 = ???????? in Roman numerals

*remember to group the pair of increased symbols together, the values of the symbols in any pair increase. The value of the new pair is:

bigger number in the pair smaller number in the pair

what is the numerical value of MCMXLIV?The subtractive principle will make the writing a lot simpler such as:

1) CLIIII = CLIV

Positional systemRoman system is a positional system, as the position of a numeral can affect the value of the number.Eg: IV = ????? VI = ????

Multiplicative principleIn Roman numeration system, horizontal bar numeral represent 1000 times the number,Eg. =11000 - 11 times of 1000. = 5000 5 times of 1000or

SISTEM PERANGKAAN HINDU ARABis a positional decimal numeral system developed between the 1st and 4th centuries by Indian mathematicianswas adopted by Persian Muslim mathematician (Al-Khwarizmi's c. 825 book On the Calculation with Hindu Numerals) and Arab mathematicians (Al-Kindi's c. 830 volumes On the Use of the Indian Numerals) by the 9th century. It later spread to the western world by the High Middle Ages.

SISTEM PERANGKAAN HINDU ARABname given to our number systemUses these numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

SISTEM PERANGKAAN HINDU ARABNumbers fr 0, 1, .12 have unique names13, 14, 19 are teens20, 21, .., 99 are combination of their earlier names Hindu Arabic system is based on 10,