NOTATION 



4291 



NOTATION 



are few notaries public, but the corresponding 

 office of commissioner of oaths is very common. 



NOTATION, no ta' shun. The manner in 

 which numbers are written is called notation, 

 and the manner of reading numbers is called 

 numeration. Our method of writing numbers, 

 using the nine digits, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 

 zero (0) has been called the Arabic notation 

 because the people of Europe got it from the 

 Arabians. But we know that the Arabians 

 never laid claim to the invention, but always 

 acknowledged it as the work of the Hindus. To 

 the Hindus we owe the. symbols and the place 

 value feature which plays so large a part in all 

 computations. 



In a cave on the top of the hill of Mana 

 Ghat in Central India the symbols were found 

 without the zero about 300 B.C. The zero ap- 

 peared about eight centuries later, and in the 

 ninth century A. D. it occurs in an inscription in 

 India. So our so-called "Arabic notation" is 

 the Hindu notation. Leonardo of Pisa (1200) 

 did much to forward the use of the Hindu no- 

 tation in Europe, but it took about two centu- 

 ries after his time for it to gain a foothold. 

 In 1350 we find "zero" in manuscript, and in 

 1491 we find it in print. The Arabic displaced 

 the Roman notation after a long struggle. 



Roman Notation. The Roman notation ex- 

 presses numbers by means of capital letters; 

 as, I, V, X, C, M. We still retain it in num- 

 bering chapters of books, volumes of books, 

 hours on clocks and in artistic numbering. The 

 following are the letters used and the value 

 they represent: 



I represents one 



V represents five 



X represents ten 



L represents fifty 



C represents one hundred 



D represents five hundred 



M represents one thousand 



(1) By placing a letter denoting a smaller 

 nn tuber in front of one denoting a larger num- 

 ber, the value of the larger number is decreased ; 

 as, I in front of X, IX, denotes ten less one 

 or 9. 



(2) When a letter denoting smaller value is 

 placed after a letter denoting greater value, the 

 great i* increased, as, II placed after 



II denotes ten plus two or 12. 



(3) A letter repeated denotes the value re- 

 peated, as, XXX is 30, CC is 200. 



(4) Placing a horizontal line over a letter 

 multiplies its value by 1000, as C denotes 

 100,000. 



Hindu Notation. This notation expresses 

 numbers by the use of ten symbols (nine dig- 

 its and zero). Because of the place value fea- 

 ture of this system, we are able to represent 

 our great series of numbers with these few sym- 

 bols: 



In the expression 222, the first 2 on the right 

 is 2 ones, the next 2 is 2 tens or 20 ones, the 

 next 2 is 2 hundreds or 200 ones. Thus any 

 symbol may express various number values, the 

 value depending upon the place the symbol 

 occupies; that is, each symbol has a value in- 

 dicated by its name and a value dependent 

 upon its place in the number. This latter value 

 is called its place value. Zero is used to desig- 

 nate the absence of any significant symbol in 

 a place; for example, three thousand four is 

 written 3004, the zeros indicating the absence of 

 hundreds and tens. 



Digits. The significant symbols are called 

 digits, also figures; thus, the number six thou- 

 sand, four hundred, fifty-two, is expressed by 

 the digits or figures, 6, 4, 5 and 2. 



Orders of Units. The successive places in a 

 number are called orders of units. The orders 

 increase from right to left in a tenfold ratio; 

 the first order is units, the second tens, the 

 third hundreds, and so on. In other words, our 

 Hindu notation is a decimal notation, decimal 

 from the Latin decem, meaning ten. 



Periods. The figures of a number are grouped 

 in periods of three figures each ; the first period 

 is cajled units' period; the second thousands' 

 period; the third millions' period; the fourth 

 billions' period; the fifth trillions' period, and 

 above that quadrillions, quint illions, sextillions, 

 septillions, octillions, and so on. 486,392,574,- 

 692,875 reads 486 trillions, 392 billions, 574 mil- 

 lions, 692 thousands, 875. The name units is 

 never read after the number of units. 



History of Notation. The various tribes and 

 nations of the earth haye had their own sys- 

 tems of expressing number. The important 

 point of distinction among the systems is the 

 base of each system. Among some low tribes 

 the base is 2, and they count 1, 2, 2 and 1, 2 

 and 2; others h:i\e the base 3 and so count 

 1, 2, 3, 3 and 1, 3 and 2, 3 and 3; many tribes 

 have the base 5 (from the fingers on one hand). 



The Hebrews used the base 10, the decimal 

 base (from fingers on both hands). In the \ al- 

 leys of the Tigris and Euphrates, 60 is found 

 as a base, 100 appearing as 60 and 40. This 

 base may be due to their knowledge of a cir< -1. : 

 they divided the circle into 360 equal parts or 

 . They knew also that 'he ndiu of 



