Online Unit Converters . It is used in counting. Numbers have been used from ancient times, first in the form of tally marks — scratches on wood or bone, and then as more abstract systems. There are several ways of expressing numbers in numeric systems. Some of them are not in use today. Different Ways of Representing Numbers. It is believed by some researchers that the concept of number was created independently in different regions.
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The original written representations of numbers through symbols evolved independently, but once trade across countries and continents became widespread, people learned and borrowed from each other and the number systems currently in use were created through collective knowledge. Hindu- Arabic Numerals. The Hindu- Arabic numeral system is one of the most widely used in the world today. It was originally developed in India and improved by the Persian and Arab mathematicians. In the Middle Ages it spread to the Western world through commerce, to replace the Roman numeral system. It was further modified and widely adopted around the world because of the European trade and colonization.
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It is a base- 1. 0 system, meaning that it is based on multiples of ten, and that it uses ten symbols to represent all numbers. Ten is a common number to use for counting because people have ten fingers, and body parts were often used for counting historically. Even today people learning to count or who want to illustrate a point about counting in conversation often use fingers. Some cultures also used toes, spaces between fingers, and knuckles for counting. It is curious that numbers are represented by “digits,” the same word that is used to refer to fingers and toes in English and in many other languages. An inscription in Latin and with Roman numerals on Admiralty Arch in London.
It reads: ANNO : DECIMO : EDWARDI : SEPTIMI : REGIS : VICTORI. They are still used today in some contexts, for example on clocks, to represent the hours. Roman numerals are based on seven numbers written with the letters of the Latin alphabet: The order is important in the Roman system because a greater number followed by the smaller means that the two need to be added, but a smaller number in front of the larger one means that the smaller number is subtracted from the larger.
For example, XI is 1. IX is 9. The subtraction rule is not universal, it only works for these numbers: IV, IX, XL, XC, CD, and CM. In some cases the subtraction rules are not used, and numerals are written in succession instead.
Systems in Other Cultures. People in many geographic areas had systems of representing numbers, similar to the Roman or the Hindu- Arabic ones. For example, some Slavic people used the Cyrillic alphabet to represent numbers such as 1 to 9, multiples of 1. The Hebrew number system uses the Hebrew alphabet to represent numbers from one to ten, multiples of ten, 1.
The rest of the numbers are represented as multiples or sums. The Greek number system is also similar.
Some cultures use simpler representations, like the Babylonian system, which has only two cuneiform symbols, for one (somewhat resembling to the letter “T”) and for ten (slightly similar to the letter “C”). So for example 3. CCCTT. The Egyptian system was very similar, except that there were additional symbols for zero, one hundred, one thousand, ten thousand, one hundred thousand, and one million, as well as special notations for fractions. Numbers in the Mayan culture had symbols for zero, one, and five, with special notation for numbers above nineteen. Unary numeral system. Tally marks in various cultures.
Unary. The unary system represents each number with the same number of symbols as its value. These symbols are usually the same, therefore if 1 is represented with A, then 5 would be represented as AAAAA. When children learn to count, their teachers often use this system to help create a link between a concrete, easy to understand system and a more abstract representation of numbers.
This system is also sometimes used in games and other simple calculations. Different countries may use different types of representation for this. For example, when keeping score of the winning teams or counting items or days, people in the Western world and some other regions would often write four vertical lines, then cross them with a fifth horizontal line, and repeat the process. For example, in part A) in the picture the person counting reached four, crossed it out, then reached four again, crossed it out, and continued to write tally marks until they added up to twelve.
People who use or have historically used Chinese characters in their writing systems, for example in China, Japan, and Korea use a certain Chinese character with five strokes to do the same. In part B) in the picture the person counts to five, completing the character, and then starts a new character, continuing the count to seven. The stroke order is pre- determined, as shown in the picture. The unary system is also used in computer science. An arithmometer that uses the decimal system and a microprocessor chip that uses the binary system. Positional System.
Positional systems work with a base. For example, in base- 1. First position is for numbers from zero to nine, that is, the number in the first position has to be multiplied by ten to the power of zero. The number in the second position is multiplied by ten to the power of one. The number in the third position is multiplied by ten to the power of two, and so on, until the numbers in all positions are exhausted. To arrive at the final value of the number represented one needs to add all the values at each position.
This is a convenient way of representing numbers because it allows one to work with numbers relatively large in value, without using large space to write them down. Example: 3. 10. 2 = 3 . It is based on two characters, “0” and “1” to represent all possible numbers. In other words it is a base- 2 system. Numbers are represented as follows: 0=0, 1=1, and from 2 the principle of addition is used. Addition in base- 2 is similar to addition in base- 1.
To increment a number by one: An artistic representation of binary numbers. If the number ends in a zero, the last zero is replaced by one: e.
Here the base- 1. If the number ends with a one but is not all ones, the first zero from the right is replaced by one, while all the ones following it on the right become zeros: 1. If the original number is all ones, then they are all changed to zeros, and a one is added at the front: 1. To add two numbers, they are aligned under each other, and for each place, 0+0 produces 0, 1+0 produces 1, and 1+1 produces 1. For example: 1. 11.
In this case, working from right to left: 1+1 produces 0, with one carried over. So, putting this together, we get 1. Subtraction works using the same principle, except instead of carrying over ones, we “borrow” ones. Multiplication is also similar to base- 1. Multiplying by 0 results in a 0, while multiplying 1 by 1 is 1. So, for example: 1. Some of the subsets below partly overlap.
Debt is a negative number. Negative Numbers. Negative numbers are numbers that represent a negative value. A minus sign is placed in front of them. For example if person A has no money and owes 5 dollars to person B, then person A has . Here –5 is a negative number.
Rational Numbers. Rational numbers are numbers that can be expressed as fractions where the denominator is a natural number that is not zero, and the numerator is an integer. For example both 3/4 and . Some examples are 3, 5, and 1. It contains 1. 7,4. Prime numbers are used in public- key cryptography, a system of encoding data, often used in online secure data exchange, such as in online banking. Interesting Facts about Numbers.
Chinese anti- fraud numbers. Anti- Fraud Numerals. To prevent fraud when writing numbers in business and commerce, Chinese language uses special complex characters that are difficult to forge by adding extra strokes. This is done because the commonly used Chinese characters for numbers are too simple and it is easy to modify their value by adding strokes.
Modern Counting in Commerce. Some languages in countries where base- 1. For example, English has a special word for twelve, “dozen” — currently used mainly for counting eggs, baked goods, wine, and flowers. Khmer has special words based on the ancient base- 2. Numeral Grouping.
Both in China and Japan the Hindu- Arabic numeral system is adopted, but large numbers are grouped by 1. In English, for example, there is a word for 1. Then follows the word million, representing 1,0.
In Japanese there is a word for 1. Unlucky Numbers. Leonardo da Vinci. Many believe that this is carried from the Judeo- Christian tradition, where thirteen was the number of Jesus Christ’s disciples during the last supper, after which the thirteenth disciple, Judas, betrayed Jesus. There was also a superstition among the Vikings that one at a thirteen people gathering will die the next year.
In Russia and many of the former Soviet countries all even numbers are considered unlucky. Possibly this tradition originated from the belief that even numbers are complete, stable and static, unmoving, and thus not alive. Odd numbers, on the other hand, represent change, motion, an entity that needs completion and progression, and life. According to this belief, it is considered bad luck to give an even number of flowers to living people — these numbers are usually reserved for funerals.
In Chinese, Japanese, and Korean- speaking countries number 4 is considered to be unlucky, because it is pronounced the same way as “death.” In some instances all numbers that have a four in them are considered unlucky. For example, a building may not have floors 4, 1. In China number 7 is also unlucky because it represents the spiritual world and ghosts. The seventh month in the Chinese calendar is referred to as the “ghost month,” when the connection between the worlds of the living and the spirits is open.