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LATEST NCERT CLASS 8 MATHS CHAPTER 3K A STORY OF NUMBERS PAGES 76, 77, 78, 79, 80

THE CHINESE NUMBER SYSTEM
The Chinese used two number systems — a written system for recording
quantities, and a system making use of rods for performing computations.
The numerals in the rod-based number system are called rod numerals.
Here we discuss the rod numerals, which are more efficient in writing
and computing with numbers than the written system of the Chinese.

The rod numerals developed in China by at least by 3rd century AD and were used till the 17th century. It was a decimal system (base-10).
The symbols for 1 to 9 were as follows:

Like the Mesopotamians, the rod numerals used a blank space to indicate the skipping of a place value. However, because of the slightly more uniform sizes of the symbols for one through nine, the blank spaces were easier to locate than in the Mesopotamian system.

Notice how similar the rod numerals are to the Hindu system. The Chinese system, with a symbol for zero, would be a fully developed place value system.

THE HINDU NUMBER SYSTEM
Where does the Hindu/Indian number system figure in the evolution of
ideas of number representation? What are its landmark numbers? And
does it use a place value system?

As can be seen, the Hindu number system is a place value system. The Hindu number system has had a symbol for 0 at least as early as 200 BCE. Because of the use of 0 as a digit, and the use of a single digit in each position, this system does not lead to any kind of ambiguity when reading or writing numerals. It is for this reason that the Hindu number system is now used throughout the world.

The use of 0 as a digit, and indeed as a number, was a breakthrough that truly changed the world of mathematics and science. In Indian mathematics, indeed, zero was not just used as a placeholder in the place
value system, but was also given the status of a number in its own right,
on par with other numbers. The arithmetic properties of the number 0
(e.g., that 0 plus any number is the same number, and that 0 times any
number is zero) were explicitly used by Aryabhata in his Āryabhaṭīya in
499 CE to compute with and do elaborate scientific computations using
Hindu numerals. The use of 0 as a number like any other number, on
which one can perform the basic arithmetic operations, was codified
by Brahmagupta in his work Brāhmasphuṭasiddhānta in 628 CE, as we
learned in an earlier grade.

By introducing 0 as a number, along with the negative numbers,
Brahmagupta created what in modern terms is called a ring, i.e., a set of
numbers that is closed under addition, subtraction, and multiplication
(i.e., any two numbers in the set can be added, subtracted, or multiplied
to get another number in that set). These new ideas laid the foundations
for modern mathematics, and particularly for the areas of algebra and
analysis.

Hopefully, this gives you a sense of all the ideas that went into writing
and computing with numbers in the way that we do today. The discovery
of 0 and the resulting Indian number system is truly one of the greatest,
most creative, and most influential inventions of all time — appearing
constantly in our daily lives and forming the basis of much of modern
science, technology, computing, accounting, surveying, and more. The
next time you are writing numbers, think about the incredible history
behind them and all the deep ideas that went into their discovery!

FIGURE IT OUT

1. Why do you think the Chinese alternated between the Zong and Heng symbols? If only the Zong symbols were to be used, how would 41 be represented? Could this numeral be interpreted in any other way if there is no significant space between two successive positions?

2. Form a base-2 place value system using ‘ukasar’ and ‘urapon’ as the
digits. Compare this system with that of the Gumulgal’s.

3. Where in your daily lives, and in which professions, do the Hindu
numerals, and 0, play an important role? How might our lives have been different if our number system and 0 hadn’t been invented or conceived of?

4. The ancient Indians likely used base 10 for the Hindu number system because humans have 10 fingers, and so we can use our fingers to count. But what if we had only 8 fingers? How would we be writing numbers then? What would the Hindu numerals look like if we were using base 8 instead? Base 5? Try writing the base-10 Hindu numeral 25 as base-8 and base-5 Hindu numerals, respectively. Can you write it in base-2?