Ancient Chinese numerals |
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Chinese Numerals
By John Kellermeier
Ancient Chinese Numerals
The earliest known form of Chinese numerals date from between 1500 and 1200 BCE. They were found on the remnants of oracular bones that were used by the priests of the Shang kings for divination by fire. These included symbols for the numbers 1 through 9, 10, 100, and 1000.
Ancient Chinese numerals
1 2 3 4 5 6 7 8 9 10 100 1000
Symbols for 20, 30, and 40 were adapted from the symbols for 2, 3, 4 and 10 as given in the following table.
20 30 40
However the symbols for 50, 60, 70, 80, and 90 were made by putting the symbol for ten on top of the symbol for the corresponding digit 5 through 9.
50 60 70 80 90
The symbol for 100 was made by putting the symbol for 1 on top of the symbol for "hundred",
. Similarly the other "hundreds" were made by putting the corresponding
digit on top of "hundred".
200 300 400 500 600 700 800 900
The thousands were made by putting a digit symbol across the symbol for "thousand" 
.
2000 3000 4000 5000 6000 7000 8000 9000
These symbols would then be put together to make the numbers form 1 to 9999. For example, the numbers 527 and 4698 would be written as
Five hundreds, two tens, and seven
Four thousands, six hundreds, nine tens, and eight
Standard Chinese Numerals
The standard Chinese numbers used today are descended from these ancient symbols. The standard system is similarly based on symbols for the numbers 1 through 9, 10, 100, 1000, and 10,000.
Standard Chinese numerals
1 2 3 4 5 6 7 8 9 10 100 1000 10,000
Unlike the ancient system, the standard system doesn't combine symbols to create hundreds and thousands but instead uses symbols in much the same way that numbers are spoken in English. For example, in English, 4698 would be read as four thousand, six hundred, ninety (nine tens) eight. In standard Chinese this would be written as
Chinese Rod Numbers
Dating from between the fourth to second centuries BCE, the Chinese also used a scientific positional number system based on symbols made up of horizontal and vertical bars that could be constructed from rods known as counting rods. By the third century CE, these rod numbers were constructed in two variations called heng and tsung numerals. The hengs were used to represent even powers of 10 (1, 100, 10000, etc.) and the tsungs were used to represent odd powers of 10 (10, 1000, 100000, etc. )
1 2 3 4 5 6 7 8 9 Hengs
1, 100, 10000, etc.Tsungs
10, 1000, 100000, etc.
These rod numbers were used on counting boards similar to a checker board with rows and columns. The rows were used to represent numbers using a base 10 positional number system starting with units to the right. For example the number 84902 would be represented as
8 4 9 0 2
Around the eighth century CE the Chinese introduced a symbol for zero probably as an influence from the Hindu number system. After this time 84902 would be represented as
8 4 9 0 2
When the rod numbers were used in written manuscripts or printed documents the numbers were written as a single symbol with the horizontal and vertical strokes joined together. For example, on a counting board the number 6287 would be represented as
6 2 8 7
When 6287 was written in a manuscript it could be condensed to
After the symbol for zero was introduced, numbers with zeros could also be written in the condensed form. The number 84902 given above could be written as
Addition with Chinese Rod Numbers
The use of these rod numbers on counting boards where the numbers were sometimes written and sometimes constructed with counting rods gave the Chinese a system for doing computations. For example, consider adding 273 and 1758.
273 1758
The rules for addition are similar to those for our contemporary number system
Without the symbol for zero, adding the numbers 273 and 1758 would be done through the following four steps
Step 1
Carries 273 1758 1 Step 2
Carries 273 1758 31
Step 3
Carries 273 1758 031
Step 4
Carries 273 1758 2031
The Chinese Abacus
Dating from about the fourteenth century CE, the Chinese abacus, or suan pan (literally "calculating board"), is a wooden frame with two decks of beads on wires. Each wire has five beads on the lower deck and two beads on the upper deck.
Beads on the upper deck are represent five each and beads on the lower deck represent one each. Numbers are made by moving the beads toward the center beam. The following gives the representation for 0 through 9 and hence the number 123,456,789.
Addition with the Chinese Abacus
To use a Chinese abacus to add we enter the first number on the abacus and then add in the digits of the second number. For example to add 2738 and 1842, we enter 2738 on the abacus.
Now we add the 2 in the units place of 1842 by sliding up two beads from bottom of the rightmost wire. This will leave a count of 10 on the first wire which needs to be carried. We then must return the beads on the first wire to the neutral positions and move up one bead from the tens wire. This gives 2740.
Now we add the tens digit, 4, from 1842 to the tens wire on the abacus. SInce there are not four beads remaining on the bottom of the tens wire to move up we must instead move down one of the two top beads and one of the bottom beads. The net effect is 5 - 1 = 4. We end up with 2780 on the abacus.
Adding the 8 from the hundreds place of 1842, we slide up three bottom beads and down one top bead. This leaves a total count of fifteen on this wire. We must carry ten by moving back the five bottom beads and one of the top beads and then moving up one of the bottom beads on the thousands wire.
Lastly we add the 1 thousand from 1842 by moving up one bottom bead on the thousand wire yielding the result of 4580.
References
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