Converting from Base 10 to Base 11 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 87425 into Base 11.
  
Solution:
                                      
The given number which is 87425 is written in Base 10. 87425 can also be written as 87425₁₀. 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 11 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Since 10 is not accepted as a single digit, then we have to use a variable to substitute a two digit number. In this case, let A = 10. Hence, the digits of Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A. If you see a subscript of 11 at the given number, then that number is written in Base 11. Base 11 number is also called undecimal system. 
      
Now, let's convert 87425 into Base 11. How? Let's divide 87425 by 11 as follows:
   
                87425 ÷ 11 = 7947 + R(8)
   
Next, let's divide the quotient, which is 7947, as follows: 
    
                 87425 ÷ 11 = 7947 + R(8)
                   7947 ÷ 11 =   722 + R(5)

Do the same thing with 722 until the quotient is 0 as follows:
   
                 87425 ÷ 11 = 7947 + R(8)
                   7947 ÷ 11 =   722 + R(5)       

                     722 ÷ 11 =     65 + R(7)
                       65 ÷ 11 =       5 + R(10 or A)
                         5 ÷ 11 =       0 + R(5)
 
The remainders will be the digits of Base 11 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  87425 = 5A758₁₁

Converting from Base 9 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 187452₉ into Base 10.
  
Solution:
                             
The given number which is 187452₉ is written in Base 9. Base 9 number is also called nonary system. The digits of Base 9 number are 0, 1, 2, 3, 4, 5, 6, 7, and 8.
   
On the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. 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. Base 10 number is a common number that we are using right now in everyday life. 
       
Now, let's convert 187452₉ into Base 10. How? Let's multiply each digits by the powers of 9 as follows:
         
Base 6 Digits:        1      8      7      4      5      2                 
Multiply by:            9⁵     9⁴     9³    9²     9¹     9⁰   
             
Add all the digits, we have
                 
(1 x 9⁵) + (8 x 9⁴) + (7 x 9³) + (4 x 9²) + (5 x 9¹) + (2 x 9⁰) = 59049 + 52488 + 5103 + 324 + 45 + 2 = 117011
             
Therefore, 187452₉ = 117011

Converting from Base 9 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 285₉ into Base 10.
  
Solution:
                             
The given number which is 285₉ is written in Base 9. Base 9 number is also called nonary system. The digits of Base 9 number are 0, 1, 2, 3, 4, 5, 6, 7, and 8.
   
On the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. 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. Base 10 number is a common number that we are using right now in everyday life. 
       
Now, let's convert 285₉ into Base 10. How? Let's multiply each digits by the powers of 9 as follows:
         
Base 6 Digits:        2      8      5                 
Multiply by:            9²     9¹     9⁰   
             
Add all the digits, we have
                 
(2 x 9²) + (8 x 9¹) + (5 x 9⁰) = 162 + 72 + 5 = 239
             
Therefore, 285₉ = 239