 THE CONCEPT OF WRITING NUMBERS,COUNTING, AND PERFORMING

THE BASIC OPERATIONS OF ADDITION, SUBTRACTION, MULTIPLICATION

AND DIVISION HAS BEEN DIRECTLY DEVELOPED BY MAN.  EVERY PERSON

IS INTRODUCED TO THESE CONCEPTS DURING HIS EDUCATION.

ONE OF THE MOST IMPORTANT FACTORS IN SCIENTIFIC DEVELOPMENT

WAS THE INVENTION OF THE DECIMAL NUMBERING SYSTEM.  THE SYSTEM

OF COUNTING IN UNITS OF TENS PROBABLY DEVELOPED BECAUSE MAN 

HAS TEN FINGERS.  THE USE OF THE NUMBER 10 AS THE BASE OF OUR

NUMBER SYSTEM IS NOT OF PRIME IMPORTANCE; ANY STANDARD UNIT 

WOULD DO AS WELL.  THE MAIN USE OF A NUMBER SYSTEM IN EARLY

TIMES WAS MEASURING QUANTITIES AND KEEPING RECORDS, NOT 

PERFORMING MATHEMATICAL CALCULATIONS.  AS THE SCIENCES DEVELOPED

OLD NUMBERING SYSTEMS BECAME MORE AND MORE OUTDATED. THE LACK OF

AN ADEQUATE NUMERICAL SYSTEM GREATLY HAMPERED THE SCIENTIFIC

DEVELOPMENT OF EARLY CIVILIZATIONS.

     TWO BASIC CONCEPTS SIMPLIFIED THE OPERATION NEEDED TO

MANIPULATE NUMBERS; THE CONCEPT OF POSITION, AND THE NUMERAL

ZERO.  THE CONCEPT OF POSITION CONSISTS OF ASSIGNING TO A NUMBER A

A VALUE WHICH DEPENDS BOTH ON THE SYMBOL AND ON ITS POSITION IN

THE WHOLE NUMBER.  FOR EXAMPLE THE DIGIT 5 HAS A DIFFERENT VALUE

IN EACH OF THE THREE NUMBERS 135, 152, AND 504.  IN THE FIRST

NUMBER, THE DIGIT 5 HAS ITS ORIGINAL VALUE 5; IN THE SECOND, IT

HAS THE VALUE OF 500, OR 5 TIMES 10 TIMES 10.  SOMETIMES A

POSITION IN A NUMBER DOES NOT HAVE A VALUE BETWEEN 1 AND 9.

IF THIS POSITION WERE SIMPLY LEFT OUT, THERE WOULD BE NO

DIFFERENCE IN NOTATION BETWEEN 709 AND 79.  THIS IS WHERE THE

NUMERAL ZERO FILLS THE GAP.  IN THE NUMBER 709. THERE ARE 7

HUNDRED, 0 TENS AND 9 UNITS.  THUS, BY USING THE CONCEPT

OF POSITION AND THE NUMERAL 0, ARITHMETIC BECOMES QUITE

EASY.

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