NOTATION AND NUMERATION. 219 



units is hundreds, and the seconds figure to the right 

 is hundredths. The third figure to the left is 

 thousands, and the third to the right is thousandths, 

 and so on. The figures equally distant from units 

 place correspond in name, but the decimals have the 

 ending ths, which distinguishes them from whole 

 numbers. The following is the numeratibn of the 

 number in the above table : nine hundred eighty- 

 seven million, six hundred fifty-four thousand, three 

 hundred twenty-one, and twenty-three million, four 

 hundred fifty-six thousand, seven hundred eighty- 

 nine hundred-millonths. 



The decimals increase to the left, on the scale of 

 ten, the same as whole numbers; for, beginning at, 

 say, 4 thousandths, in the table, the next figure to 

 the left is hundreths, which is ten times as great, 

 and the next tenths, or ten times the hundreths, 

 and so on through both decimals and whole num- 

 bers. 



Principles of Decimals. 



4. The value of a decimal is not changed by an- 

 nexing or rejecting a cipher to the right of the last 

 figure. 



Explanation. 



(a). The decimal .8 equals 8/10, which reduced, 

 equals 4/5. 



(b). Adding one cipher we get .80, which equals 

 80/100, which reduced, equals 4/5. 



(c). Consequently, if both .8 and .80 can be re- 

 duced to 4/5, they are equal and adding a cipher 

 has not changed the value. 



