Converting from Base 6 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 452013₆ into Base 10.
  
Solution:
                             
The given number which is 452013₆ is written in Base 6. Base 6 number is also called heximal system. The digits of Base 6 number are 0, 1, 2, 3, 4, and 5.
   
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 452013₆ into Base 10. How? Let's multiply each digits by the powers of 6 as follows:
         
Base 6 Digits:        4      5      2      0      1      3                 
Multiply by:            6⁵     6⁴     6³    6²     6¹     6⁰   
             
Add all the digits, we have
                 
(4 x 6⁵) + (5 x 6⁴) + (2 x 6³) + (0 x 6²) + (1 x 6¹) + (3 x 6⁰) = 31104 + 6480 + 432 + 0 + 6 + 3 = 38025
             
Therefore, 452013₆ = 38025

Converting from Base 6 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 245₆ into Base 10.
  
Solution:
                             
The given number which is 245₆ is written in Base 6. Base 6 number is also called heximal system. The digits of Base 6 number are 0, 1, 2, 3, 4, and 5.
   
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 245₆ into Base 10. How? Let's multiply each digits by the powers of 6 as follows:
         
Base 6 Digits:        2      4      5                 
Multiply by:            6²     6¹     6⁰   
             
Add all the digits, we have
                 
(2 x 6²) + (4 x 6¹) + (5 x 6⁰) = 72 + 24 + 5 = 101
             
Therefore, 245₆ = 101 

Converting from Base 10 to Base 6 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 148506 into Base 6.
  
Solution:
                                      
The given number which is 148506 is written in Base 10. 148506 can also be written as 148506₁₀. 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 6 number is a number whose digits are 0, 1, 2, 3, 4, and 5. If you see a subscript of 6 at the given number, then that number is written in Base 6. Base 6 number is also called heximal system. 
      
Now, let's convert 148506 into Base 6. How? Let's divide 148506 by 6 as follows:
   
                148506 ÷ 6 = 24751 + R(0)
   
Next, let's divide the quotient, which is 24751, as follows: 
    
                148506 ÷ 6 = 24751 + R(0)
                  24751 ÷ 6 =   4125 + R(1)
 
Do the same thing with 4125 until the quotient is 0 as follows:
   
                 148506 ÷ 6 = 24751 + R(0)
                   24751 ÷ 6 =   4125 + R(1) 
                     4125 ÷ 6 =     687 + R(3) 
                       687 ÷ 6 =     114 + R(3) 

                       114 ÷ 6 =       19 + R(0)

                         19 ÷ 6 =         3 + R(1)

                           3 ÷ 6 =         0 + R(3)

                  
The remainders will be the digits of Base 6 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  148506 = 3103310₆

Converting from Base 10 to Base 6 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 699 into Base 6.
  
Solution:
                                      
The given number which is 699 is written in Base 10. 699 can also be written as 699₁₀. 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 6 number is a number whose digits are 0, 1, 2, 3, 4, and 5. If you see a subscript of 6 at the given number, then that number is written in Base 6. Base 6 number is also called heximal system. 
      
Now, let's convert 699 into Base 6. How? Let's divide 699 by 6 as follows:
   
                699 ÷ 6 = 116 + R(3)
   
Next, let's divide the quotient, which is 116, as follows: 
    
                699 ÷ 6 = 116 + R(3)
                116 ÷ 6 =   19 + R(2)
 
Do the same thing with 19 until the quotient is 0 as follows:
   
                699 ÷ 6 = 116 + R(3)
                116 ÷ 6 =   19 + R(2)                   

                  19 ÷ 6 =     3 + R(1)

                    3 ÷ 6 =     0 + R(3) 

   
The remainders will be the digits of Base 6 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  699 = 3123₆

Converting from Base 5 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 334421₅ into Base 10.
  
Solution:
                             
The given number which is 334421₅ is written in Base 5. Base 5 number is also called quinary system. The digits of Base 5 number are 0, 1, 2, 3, and 4.
   
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 334421₅ into Base 10. How? Let's multiply each digits by the powers of 5 as follows:
         
Base 5 Digits:        3      3      4      4      2      1              
Multiply by:            5⁵     5⁴     5³    5²     5¹     5⁰  
             
Add all the digits, we have
                 
(3 x 5⁵) + (3 x 5⁴) + (4 x 5³) + (4 x 5²) + (2 x 5¹) + (1 x 5⁰) = 9375 + 1875 + 500 + 100 + 10 + 1 = 11861
             
Therefore, 334421₅ = 11861