Converting from Base 10 to Base 8 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 299012 into Base 8.
  
Solution:
                                      
The given number which is 299012 is written in Base 10. 299012 can also be written as 299012₁₀. 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 8 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, and 7. If you see a subscript of 8 at the given number, then that number is written in Base 8. Base 8 number is also called octal system. 
      
Now, let's convert 299012 into Base 8. How? Let's divide 299012 by 8 as follows:
   
                299012 ÷ 8 = 37376 + R(4)
   
Next, let's divide the quotient, which is 37376, as follows: 
    
                299012 ÷ 8 = 37376 + R(4)
                  37376 ÷ 8 =   4672 + R(0)
 
Do the same thing with 4672 until the quotient is 0 as follows:
   
                299012 ÷ 8 = 37376 + R(4)
                  37376 ÷ 8 =   4672 + R(0)
                    4672 ÷ 8 =     584 + R(0) 
                      584 ÷ 8 =       73 + R(0) 

                        73 ÷ 8 =         9 + R(1)

                          9 ÷ 8 =         1 + R(1)

                          1 ÷ 8 =         0 + R(1)

                  
The remainders will be the digits of Base 8 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  299012 = 1110004₈

Converting from Base 10 to Base 8 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 987 into Base 8.
  
Solution:
                                      
The given number which is 987 is written in Base 10. 987 can also be written as 987₁₀. 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 8 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, and 7. If you see a subscript of 8 at the given number, then that number is written in Base 8. Base 8 number is also called octal system. 
      
Now, let's convert 987 into Base 8. How? Let's divide 987 by 8 as follows:
   
                987 ÷ 8 = 123 + R(3)
   
Next, let's divide the quotient, which is 123, as follows: 
    
                987 ÷ 8 = 123 + R(3)
                123 ÷ 8 =   15 + R(3)

Do the same thing with 15 until the quotient is 0 as follows:
   
                987 ÷ 8 = 123 + R(3)
                123 ÷ 8 =   15 + R(3)             

                  15 ÷ 8 =     1 + R(7)
                    1 ÷ 8 =     0 + R(1)
   
The remainders will be the digits of Base 8 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  987 = 1733₈

Converting from Base 7 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 512035₇ into Base 10.
  
Solution:
                             
The given number which is 512035₇ is written in Base 7. Base 7 number is also called heptimal system. The digits of Base 7 number are 0, 1, 2, 3, 4, 5, and 6.
   
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 512035₇ into Base 10. How? Let's multiply each digits by the powers of 7 as follows:
         
Base 6 Digits:        5      1      2      0      3      5                 
Multiply by:            7⁵     7⁴     7³    7²     7¹     7⁰   
             
Add all the digits, we have
                 
(5 x 7⁵) + (1 x 7⁴) + (2 x 7³) + (0 x 7²) + (3 x 7¹) + (5 x 7⁰) = 84035 + 2401 + 686 + 0 + 21 + 5 = 87148
             
Therefore, 512035₇ = 87148