Download presentation Babylonian number system. History of number systems. the Babylonian sexagesimal system two thousand years before our era, in another great civilization - the Babylonian - people wrote down. Translation of numbers from one number system to another

Babylonian sexagesimal system Two thousand years before our era, in another great civilization - Babylonian - people wrote numbers differently. The numbers in this number system were made up of signs of two types: Straight wedge Straight wedge (served to denote units) Recumbent wedge Recumbent wedge (to denote tens) The number 60 The number 60 was denoted by the sign that 1

To determine the value of a number, it was necessary to divide the image of the number into digits from right to left. The alternation of groups of identical characters ("digits") corresponded to the alternation of digits: The value of the number was determined by the values ​​of its constituent "digits", but taking into account the fact that the "digits" in each subsequent digit meant 60 times more than the same "digits" in the previous digit .

1. Number Number 92 = was written like this: 2. Number Number 444 looked like: FOR EXAMPLE: 444 = 7* The number consists of two digits

Additional information was needed to determine the absolute value of the number. Subsequently, the Babylonians introduced a special symbol to indicate the missing sixdecimal digit, which corresponds in the decimal system to the appearance of the number 0 in the number entry. The number 3632 was written as follows: At the end of the number, this character was usually not put. The Babylonians never memorized the multiplication table, because it was almost impossible to do so. When calculating, they used ready-made multiplication tables.

Babylonian hexadecimal The Babylonian hexadecimal system is the first number system known to us based on the positional principle. The Babylonian system played a large role in the development of mathematics and astronomy, traces of which have survived to this day. So, we still divide an hour into 60 minutes, and a minute into 60 seconds. We divide the circle into 360 parts (degrees).

ROMAN SYSTEM In the Roman system, the numbers 1, 5, 10, 50, 100, 500 and 1000 use the capital Latin letters I, V, X, L, C, D and M (respectively), which are the "digits" of this number system. A number in the Roman numeral system is denoted by a set of consecutive "numbers".

DECIMAL NUMBERS To write numbers, ten different characters are used: the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Once the writing of numbers was like this: Such an image of decimal digits is not accidental. Each digit denotes a number corresponding to the number of corners in it.

YASAKCHNYE LETTERS In the old days in Russia, among the common people, number systems were widely used, vaguely reminiscent of the Roman one. With their help, tax collectors filled out tax receipts - yasak (yasak letters) and made notes in a tax notebook. kopeck ten kopecks one ruble ten rubles one hundred rubles 232 rubles 24 kopecks

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HISTORY OF NUMBER SYSTEMS

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Babylonian sexagesimal system

Two thousand years before our era, in another great civilization - the Babylonian - people wrote numbers differently.
Numbers in this number system were composed of signs of two types:
Straight wedge (served to indicate units)

Recumbent wedge (for tens)

The number 60 was denoted by the sign, as 1

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To determine the value of a number, it was necessary to divide the image of the number into digits from right to left. The alternation of groups of identical characters ("numbers") corresponded to the alternation of digits:

The value of the number was determined by the values ​​of its constituent "digits", but taking into account the fact that the "digits" in each subsequent digit meant 60 times more than the same "digits" in the previous digit.

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1. The number 92 = 60 + 32 was written like this:

2. The number 444 looked like:

FOR EXAMPLE:

444 \u003d 7 * 60 + 24. The number consists of two digits

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Additional information was needed to determine the absolute value of the number.
Subsequently, the Babylonians introduced a special symbol to indicate the missing sixdecimal digit, which corresponds in the decimal system to the appearance of the number 0 in the notation of the number.

The number 3632 was written like this:

This symbol was usually not put at the end of the number.
The Babylonians never memorized the multiplication table, because it was almost impossible to do so. When calculating, they used ready-made multiplication tables.

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The sixagesimal Babylonian system is the first number system known to us based on the positional principle.

The Babylonian system played a large role in the development of mathematics and astronomy, traces of which have survived to this day. So, we still divide an hour into 60 minutes, and a minute into 60 seconds.
We divide the circle into 360 parts (degrees).

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ROMAN SYSTEM

In the Roman system, the numbers 1, 5, 10, 50, 100, 500, and 1000 use the capital Latin letters I, V, X, L, C, D, and M (respectively), which are the "digits" of this number system. A number in the Roman numeral system is denoted by a set of consecutive "numbers".

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Calendar on a stone slab (3rd - 4th centuries), found in Rome

History of numbers and number systems Number systems A number system is a way of writing numbers using special characters - numbers. Numbers: 123, 45678, 1010011, CXL Numbers: 0, 1, 2, … I, V, X, L, … An alphabet is a set of numbers. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Types of number systems: - non-positional - the value of a digit does not depend on its place (position) in the notation of the number; - positional - the value of a digit depends on its place (position) in the notation of the number; Non-positional number systems Unary number system Unary - one digit denotes a unit (1 day, 1 stone, 1 ram, ...) At the excavations of the sites of ancient people, archaeologists find images in the form of serifs, dashes on solid surfaces: stone, clay, wood - this was considered so our ancestors some objects, bags, cattle. Ancient Egyptian decimal non-positional system Try to learn and read this number? 2521 Roman numeral system I - 1 (finger), V - 5 (open palm, 5 fingers), X - 10 (two palms), L - 50, C - 100 (Centum), D - 500 (Demimille), M - 1000 (Mille) Rules: – (usually) do not put more than three identical digits in a row – if the low digit (only one!) is to the left of the high digit, it is subtracted from the sum (partially non-positional!) Example: 2381 = MMCCCLXXXI Alphabetical number systems Slavic system numerals Positional number systems Duodecimal system In Russia, the score was kept by dozens, remember what a DOZHIN equals? 12 And where else do we meet the duodecimal number system? A year is 12 months, half a day is 12 hours, sets and cutlery are designed for 12 people. Babylonian sexagesimal system Numbers in this number system were composed of signs of two types: a straight wedge served to designate units, and a recumbent wedge - to designate tens. The number 32, for example, was written like this: Signs and served as numbers in this system. The number 60 was again denoted by the same sign as 1, the same sign was used for the numbers 3600, 216000 and all other powers of 60. Therefore, the Babylonian number system was called sexagesimal. To determine the value of a number, it was necessary to divide the image of the number into digits from right to left. A new discharge began with the appearance of a straight wedge after a recumbent one, if we consider the number from right to left. Decimal system It appeared in India in \/ century AD. and it arose after the appearance of the number 0, which was invented by Greek astronomers to indicate the missing value. Later, the Arabs got acquainted with this number system. They appreciated it, began to use it and brought it to Europe in the 12th century. And since that time, mankind has been using this number system. Decimal 0,1,2,3,4,5,6,7,8,9 Binary system With the advent of computer science, computer technology, the 2nd number system has found its application, the roots of which go back to ancient China. What is the base of this number system? What numbers are used in the record? 2, the numbers are 0 and 1. Why is it used in computer science? Associated with the encoding of information: writing to disk, transmission of electrical signals. Binary 2 0.1 Hours in the binary system "BROKING" your head Read the poem by A.N. Starikov: She was 1100 years old, She went to the 101st grade, In a portfolio of 100 books she wore All this is true, not nonsense. When, dusting with a dozen legs, She walked along the road, A puppy always ran after her With one tail, but 100-legged. She caught every sound With her 10 ears, And 10 tanned hands Holding a briefcase and a leash. And 10 dark blue eyes Examined the world habitually ... But everything will become quite ordinary, When you understand our story. Did you understand the poet's story? 11002 =1210; 1012 = 510 1002 = 410 102 = 210 Interesting problem A monkey hangs on its tail and chews bananas. There are 101 bananas in each hand, and 1 more banana in each leg than in the hand. How many bananas does a monkey have? Thank you for your attention

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Babylonian sexagesimal system

Two thousand years before our era, in another great civilization - the Babylonian - people wrote numbers differently. The numbers in this number system were composed of two types of signs: Direct wedge (served to indicate units) Recumbent wedge (to indicate tens) The number 60 was indicated by the sign, which is the same as 1

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To determine the value of a number, it was necessary to divide the image of the number into digits from right to left. The alternation of groups of identical characters ("digits") corresponded to the alternation of digits: The value of the number was determined by the values ​​of its constituent "digits", but taking into account the fact that the "digits" in each subsequent digit meant 60 times more than the same "digits" in the previous digit .

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1. The number 92 = 60 + 32 was written as follows: 2. The number 444 looked like: FOR EXAMPLE: 444 = 7 * 60 + 24. The number consists of two digits

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Additional information was needed to determine the absolute value of the number. Subsequently, the Babylonians introduced a special symbol to indicate the missing sixdecimal digit, which corresponds in the decimal system to the appearance of the number 0 in the notation of the number. The number 3632 was written like this: At the end of the number, this character was usually not put. The Babylonians never memorized the multiplication table, because it was almost impossible to do so. When calculating, they used ready-made multiplication tables.

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The sixagesimal Babylonian system is the first number system known to us based on the positional principle. The Babylonian system played a large role in the development of mathematics and astronomy, traces of which have survived to this day. So, we still divide an hour into 60 minutes, and a minute into 60 seconds. We divide the circle into 360 parts (degrees).

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ROMAN SYSTEM

In the Roman system, the numbers 1, 5, 10, 50, 100, 500, and 1000 use the capital Latin letters I, V, X, L, C, D, and M (respectively), which are the "digits" of this number system. A number in the Roman numeral system is denoted by a set of consecutive "numbers".

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Roman numerals table

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Calendar on a stone slab (3rd - 4th centuries), found in Rome

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DECIMAL NUMBER SYSTEM

To write numbers, ten different characters are used: the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Once the spelling of numbers was like this: Such an image of decimal digits is not accidental. Each digit denotes a number corresponding to the number of corners in it.

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DISCLOSURES

In the old days in Russia, among the common people, number systems were widely used, vaguely reminiscent of the Roman one. With their help, tax collectors filled out tax receipts - yasak (yasak letters) and made notes in a tax notebook. kopeck ten kopecks one ruble ten rubles one hundred rubles 232 rubles 24 kopecks

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