DENOMINATE NUMBERS 



1706 



DENOMINATE NUMBERS 



noon of one day to noon of the next, at a 

 given place, noon meaning the moment of the 

 sun's crossing the meridian of that place. The 

 mean solar year is 365 days, 5 hours, 48 min- 

 utes, 46 seconds, or nearly 3f>5 l A days. The 

 common year contains 365 days; leap year, 366 

 days. This is explained fully in the article 

 CALENDAR. 



Angular Measurement. In the measurement 

 of angles the most important unit employed 

 is the degree. 



FIG. 10 



In Fig. 10 the line OA is perpendicular to the 

 line CB, and the angle AOB is a right angle. 

 This angle is measured by the arc AB, or one- 

 fourth of a circumference, and since every cir- 

 cumference is divided into 360 degrees (360), 

 it is an angle of 90. Any angle less than a 

 right angle is measured by less than one-fourth 

 of a circumference, and so is less than 90. 

 Any angle greater than a right angle is meas- 

 ured by more than one-fourth of a circumfer- 

 ence and is more than 90, as seen below 

 (Fig. 11). 



FIG. 



The angle AOD is an angle of 45, and AOC 

 is an angle of 135. 



Table of Angular Measure 



60 seconds (") = 1 minute (') 

 60 minutes =1 degree () 



360 degrees =4 right angles or 1 circum- 



ference 



Reduction of Denominate Numbers. The 

 process of reducing denominate numbers to 



lower denominations or units is called reduction 

 descending; as, 6 feet=72 inches. The process 

 of reducing them to higher denominations or 

 units is called reduction ascending ; as, 16 pints 

 =8 quarts. The latter reduction is used the 

 more often. 



Reducing to a lower unit. (1) Express 16 ft. 

 in inches: 



Number of inches=16Xl2=192 



or 

 16 ft. = 16X!2 in. = 192 in. 



(2) Change 9 ft. 8 in. to inches. 

 Number of inches= (9X 12) +8 = 116. 



(3) Express in ounces avoirdupois 7 Ib. 8 oz. 

 Number of ounces= (7x16) +8 = 120. 



(4) Express as square inches: 9 sq. ft. 123 

 sq. in. 



Number sq. in. = (9x144) +123 = 1419 



or 



9 sq. ft. + 123 sq. in.= (9x144) sq. In. + 123 

 sq. in. or 1419 sq. in. 



The work is done without names thus : 



144 

 X9 



1296 

 + 123 



1419 



The most desirable form for such problems is 

 that in which the words are at the left-hand 

 side of the equality .sign and no words are 

 attached to numbers, as: 



Number of sq. in.= (9 X 144) +123 = 1419. 



(5) Express as seconds, 3 da. 7 hr. 50 min. 

 8 sec. 



Number hr.= (3X24) +7 = 79. 

 Number min.= (79 X60) +50 = 4790. 

 Number sec.= (4790x60) +8 = 287408. 



The work done without names is as follows: 





24 

 X3 



72 

 + 7 



79 

 X60 



4740 

 + 50 



4790 

 X60 



287400 

 + 8 



79 4790 287408 



Reducing to higher units. (1) Change to feet 

 (a) 216 in.; (b) 7 ft. 9 in. 



(a) Number ft.= =^= 



(b) Number ft.= 



'l2 = 'i- 



(2) Change to pounds avoirdupois (a) 432 

 oz.; (b) 71b. 15 oz. 



(a) Number lb. = ^-=27. (b) Number Ib. 

 _15 



