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Saturday, July 25, 2015

Converting from Base 10 to Base 5 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"


Convert 745286 into Base 5.
  
Solution:
                                      
The given number which is
745286 is written in Base 10. 745286 can also be written as 74528610. If you don't see any subscript at the given number, then that number is written in Base 10. Base 10 number is also called decimal system.  The digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10 number is a common number that we are using right now in everyday life. 
   
On the other hand, Base 5 number is a number whose digits are 0, 1, 2, 3, and 4. If you see a subscript of 5 at the given number, then that number is written in Base 5. Base 5 number is also called quinary system. 
      
Now, let's convert
745286 into Base 5. How? Let's divide 745286 by 5 as follows:
   
               
745286 ÷ 5 = 149057 + R(1)
   
Next, let's divide the quotient, which is 149057, as follows: 
    
                745286
÷ 5 = 149057 + R(1)
                149057 ÷ 5 =   29811 + R(2)
 
Do the same thing with 29811 until the quotient is 0 as follows:
   
               
745286 ÷ 5 = 149057 + R(1)
                149057 ÷ 5 =   29811 + R(2)

                  29811 ÷ 5 =     5962 + R(1)
                    5962 ÷ 5 =     1192 + R(2) 
                      1192 ÷ 5 =       238 + R(2) 
                      238 ÷ 5 =         47 + R(3)   
                        47 ÷ 5 =           9 + R(2)  
                          9 ÷ 5 =           1 + R(4)  
                          1 ÷ 5 =           0 + R(1)     
               
  
The remainders will be the digits of Base 5 number. Use the digits of the remainders from bottom to top. Therefore,
   
                 
745286 = 1423221215