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Base Ten Number System

Early Indian non place value numeral forms for

the digits 1-9 date back to the 1st century B.C.

It wasnt until around 629 A.D. that Bhaskara

introduces the idea of place value.

Originated from the Hindu-Arabic numeration

system. Fibonacci brought it to the Europeans in

the 1200s, adding a name for the place values and

adding a zero.

Base 10 (Decimal) Numbering System The Indian

culture developed the decimal system. The Mohenjo

Daro culture of the Indus valley was using a form

of decimal numbering some 5000 years ago.

Succeeding cultural changes in this area

developed the decimal system into a rigorous

numbering system, including the use of zero by

the Hindu mathematicians some 1500 years ago. The

digits we use for the decimal system are the

Arabic/Indian digits of 0 thru 9. Each number

occupies a place value. When 1 is reached, the

value goes to 0 and 1 is added to the next place

value. 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17

,18,19,20,etc

Each place value to the left is equal to 10 times

the place value to the right. Which implies that

each place value to the right is equal to the

place value to the left divided by10.

This gives great precision for a number. The

precision gained from this numbering system

played no small part in the development of the

calculus.

This gives great precision for a number. The

precision gained from this numbering system

played no small part in the development of the

calculus.

A zero was used in the decimal system to

represent nothing of a particular place

value. The use of 10 digits for a numbering

system may be seen to arise from counting on our

10 fingers. Count on your fingers up to ten, put

a mark in the sand and continue counting on

fingers.

- Decimal writers
- c. 3500 - 2500 BC Elamites of Iran possibly used

early forms of decimal system.23 - c. 2900 BC Egyptian hieroglyphs show counting in

powers of 10 (1 million 400,000 goats, etc.)

see Ifrah, below - c. 2600 BC Indus Valley Civilization, earliest

known physical use of decimal fractions in

ancient weight system 1/20, 1/10, 1/5, 1/2. See

Ancient Indus Valley weights and measures - c. 1400 BC Chinese writers show familiarity with

the concept for example, 547 is written 'Five

hundred plus four decades plus seven of days' in

some manuscripts - c. 1200 BC In ancient India the Vedic text

Yajur-Veda states the powers of 10, up to 1055 - c. 400 BC Pingala develops the binary number

system for Sanskrit prosody, with a clear mapping

to the base-10 decimal system - c. 250 BC Archimedes writes the Sand Reckoner,

which takes decimal calculation up to

1080,000,000,000,000,000 - c. 100200 The Satkhandagamawritten in India

earliest use of decimal logarithms - c. 476550 Aryabhata uses an alphabetic cipher

system for numbers that used zero - c. 598670 Brahmagupta explains the

Hindu-Arabic numerals (modern number system)

which uses decimal integers, negative integers,

and zero - c. 780850 Mu?ammad ibn Musa al-?warizmi first

to expound on algorism outside India - c. 920980 Abu'l Hasan Ahmad ibn Ibrahim

Al-Uqlidii earliest known direct mathematical

treatment of decimal fractions. - c. 13001500 The Kerala School in South India

decimal floating point numbers - 1548/491620 Simon Stevin author of De Thiende

('the tenth') - 15611613 Bartholemaeus Pitiscus (possibly)

decimal point notation. - 15501617 John Napier use of decimal logarithms

as a computational tool - 1765 Johann Heinrich Lambert discusses (with

few if any proofs) patterns in decimal expansions

of rational numbers and notes a connection with

Fermat's little theorem in the case of prime

denominators - 1800 Karl Friedrich Gauss uses number theory to

systematically explain patterns in recurring

decimal expansions of rational numbers (e.g., the

relation between period length of the recurring

part and the denominator, which fractions with

the same denominator have recurring decimal parts

which are shifts of each other, like 1/7 and 2/7)

and also poses questions which remain open to

this day (e.g., a special case of Artin's

conjecture on primitive roots is 10 a generator

modulo p for infinitely many primes p?).

Resources

http \\dpsnas01\gwhs_top\gwhs_data\registergw\Des

ktop\Base 10 (Decimal).htm http//www.istockphoto.

com/file_thumbview_approve/2991716/2/istockphoto_2

991716_ten_fingers.jpg http//en.wikipedia.org/wik

i/Base_ten

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