Converting from Base 10 to Base 7 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 306 into Base 7.
  
Solution:
                                      
The given number which is 306 is written in Base 10. 306 can also be written as 306₁₀. 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 7 number is a number whose digits are 0, 1, 2, 3, 4, 5, and 6. If you see a subscript of 7 at the given number, then that number is written in Base 7. Base 7 number is also called heptimal system. 
      
Now, let's convert 306 into Base 7. How? Let's divide 306 by 7 as follows:
   
                306 ÷ 7 = 43 + R(5)
   
Next, let's divide the quotient, which is 43, as follows: 
    
                306 ÷ 7 = 43 + R(5)
                  43 ÷ 7 =   6 + R(1)

Do the same thing with 6 until the quotient is 0 as follows:
   
                306 ÷ 7 = 43 + R(5)
                  43 ÷ 7 =   6 + R(1)             

                    6 ÷ 7 =   0 + R(6)

   
The remainders will be the digits of Base 7 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  306 = 615₇

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