CONVERSION OF NUMBERS FROM ONE SCALE TO ANOTHER. ] gj 



We have, therefore, no difficulty in transforming a num- 

 ber from any other scale to our own. But it s not so easy The converse 

 to convert a number from the decimal to another notation, n^ore difficult, 

 though the operation is of a similar nature ; but the diffi- 

 culty arises in our not being so ready in the use of the 

 other scales. 



In this case the given number is always of the form 10"a R"I«' 

 -t- 10"-*6 + lO^'^c, &c., and the readiest way to transform it 

 is, first to convert each of the powers of 10, beginning with 

 the lowest, into the required scale, then each of the 

 given terms in the formula into the same, the sum of which 

 will be the answer. When it is only necessary to observe, 

 that in all the operations of multiplication, and addition, we 

 must divide by the radix of the system, setting down the 

 overplus, and carrying the quotient, instead of dividing by 

 JO, as is done in common arithmetic. 



As an example, let it be required to transform 1728 to the Example 4. 

 duodenary scale. 



First 10 =z (p 



10* zr 9 X ?> = 84 

 10' — 84 X ?» =: 6 7 4 



10* = 67.4 X <p = 5954 



&c. 



Also 1728 = 10» -f 10*.7 + 10.2 + 8. 



8 = 8 rr 8 



10. 2 = 9 X 2 rr 18 

 10*.7 = 84 X 7 = 4^4 

 10^1 — 6y 4 X 1 = 6y4 



therefore 1728 = 1000 Jns, 



This example being understood, the transformation in 

 other cases will become very easy : thus in the following 

 examples, transform 71671 to the duodensiry scale. 



First, 71671 = 10^7 + 10^I + 10^6 + 10.7 + 1. ExampUS. 



Now 



