CHAPTER 1. 

 Decimals — Notation and Numeration. 



1. A decimal, or a decimal fraction, is a fraction 

 whose denominator is 10, 100, 1,000, etc. 



2. The denominator is always 10 or a multiple 

 of 10, and is not expressed as in common fractions, 

 by writing it under the numerator, with a line be- 



3 3 3 



tween them, as — , , . The denominator is 



10 100 1000 

 always understood, the numerator consisting of the 

 figures on the right of the unit figure of the number. 

 In order to distinguish the unit figure, a period (.), 

 called the decimal point, is placed between the unit 

 figure and the next figure on the right. The decimal 

 point may be regarded in two wa^/s : First, as indi- 

 cating that the number on the right is the numerator 

 of a fraction whose denominator is 10, 100, 1,000, 

 etc. ; and, second, as a part of the Arabic system of 

 notation, each figure on the right being 10 times as 

 large as the next succeeding figure, and 10 times as 

 small as the next preceding figure, serving merely 

 to point out the unit figure. 



3. The reading of a decimal depends upon the 

 number of decimal places in it; i. e., upon the num- 

 ber of figures to the right of the unit figure. 



The first figure to the right of the unit figure ex- 

 presses tenths. 



The second figure to the right of the unit ex- 

 presses hundreths. 



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