DECEMVIRS 



1730 



DECIMAL FRACTIONS 



DECEMVIRS, desem'vcrz, a term which 

 might be applied to any official body of ten 

 men (from dccem, meaning ten), but having 

 specific reference to the ten magistrates ap- 

 pointed in 451 B.C., with absolute powers for 

 one year, to systematize the laws of Rome. 

 The first commission governed with wisdom 

 and moderation, but its successors were ex- 

 tremely unpopular, their violence and despot- 

 ism leading to an insurrection and the abolish- 

 ment of the office in 449 B.C. 



DECIDUOUS, desid'uus, TREES, those 

 trees which lose and renew all their leaves 

 each year at definite seasons, as the oak, ash, 

 beech, birch, elm and many others which are 

 familiar to everyone. The term deciduous 

 is from Latin words which mean something 

 which falls down. In temperate countries most 

 deciduous trees lose their leaves in the autumn, 

 or fall of the year, leaving twigs and branches 

 bare in winter; in the spring they don a new 

 garb of green. In certain other countries the 

 falling of the leaves is governed by times of 

 drought, etc. 



The falling of the leaves is caused by the 

 formation of a waterproof layer of tissue where 

 the leaf joins the twig, as a result of which 

 the leaf is cut off from its source of supply. 

 It then has a weaker hold on the twig and the 

 winds loosen it. See LEAVES. 



Those trees which have a covering of leaves 

 all the year are called evergreens (see EVER- 

 GREEN). 



DECIMAL FRACTIONS. Our system of 

 writing numbers is a decimal system. (For a 

 full discussion of this, see NOTATION.) Since 

 a clear understanding of our decimal notation 

 is essential to an intelligent attack upon deci- 

 mal fractions, a short review of it is given 

 here. 



Place value is the idea underlying the sys- 

 tem of notation. The number expressed by 



abc 



222 is 200+20+2. The value of b is 10 times 

 as great as that of c; the value of a is 10 times 

 as great as that of b. A digit represents so 

 many ones, or so many tens, or so many 

 hundreds, and so on, according to the column, 

 or "place," it occupies. Read the lettered 



ab 



digits, giving their full number values: 7886; 

 a reads 800; b reads 80. b is Ho as large as a. 



abc 



In the expression 6444 a reads 400; b reads 40; 

 c reads 4 ; c is Ho as great as b ; b is Mo as 

 great as a. 



Much of this reading should precede the 



study of decimal fractions, and there should 

 also be work such as the following: Read the 

 underlined, giving full value: 7836; 9248; 

 4924; 73926. They read 800, 30;~90007 40; 

 4000, 4; 3000, 20. 



Read, giving full value to each part, and 

 write as you read, indicating this full value: 

 7936=7000+900+30+6. Write in column 

 form: 



7000 



900 



30 



7936 



It took the human race about twelve cen- 

 turies to. take the step from writing whole 

 numbers in a decimal system to writing frac- 

 tions in the same system. The decimal frac- 

 tion appeared in the sixteenth century, and 

 it was not until the eighteenth that it w 

 recognized in the schools. The nineteenth cen- 

 tury brought it into somewhat general use, 

 but the early twentieth century sees it sup- 

 planting generally the common fraction in the 

 scientific and industrial world. 



Let us examine the method of transition 

 from the decimal notation applied to whole 

 numbers, to the same applied to fractions. In 



abc 



the expression 111, c is Ho of b; b is Ho of o. 

 It is desired to write a number which is Ho 



abed 



of c. Place 1 to the right of c and have 1111 ; 

 by this transaction the original number 111 

 is changed to 1111 ; that is, c has changed from 

 1 to 10, and b from 10 to 100 and a from 100 

 to 1000. But we wish to write a number that is 

 Ho of c, and not change the value of the orig- 

 inal number 111. How can it be done? In 

 other words, how can we write lllHo, using 

 the decimal system employed in writing whole 

 numbers? Here are several of the ways used 

 in the sixteenth and seventeenth centuries: 



01 



lllll ; 1111; 1111; 111 1 ; 111 1 ; 

 01 



and there were other methods. Below are 

 given some illustrations of decimals, whole and 

 fractional, as they appeared in the early dajs 

 of decimal fractions: 



123 



7186|47_; 7186847; 7186847; 71868 1 4 2 7 3 ; 



each reads seven thousand one hundred eighty- 

 six and eight hundred forty-seven thousandths, 

 although the early writers read the fractions at 

 first 8-tenths, 4-hundredths, 7-thousandths. 



This short historical review shows that the 

 great difficulty of the men who first tried to 

 write decimal fractions was to find a means of 



