Converting from Base 5 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 431₅ into Base 10.
  
Solution:
                             
The given number which is 431₅ 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 431₅ into Base 10. How? Let's multiply each digits by the powers of 5 as follows:
         
Base 5 Digits:        4      3      1              
Multiply by:            5²     5¹     5⁰   
             
Add all the digits, we have
                 
(4 x 5²) + (3 x 5¹) + (1 x 5⁰) = 100 + 15 + 1 = 116
             
Therefore, 431₅ = 116

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

Converting from Base 10 to Base 5 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 875 into Base 5.
  
Solution:
                                      
The given number which is 875 is written in Base 10. 875 can also be written as 875₁₀. 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 875 into Base 5. How? Let's divide 875 by 5 as follows:
   
                875 ÷ 5 = 175 + R(0)
   
Next, let's divide the quotient, which is 175, as follows: 
    
                875 ÷ 5 = 175 + R(0)
                175 ÷ 5 =   35 + R(0)
 
Do the same thing with 35 until the quotient is 0 as follows:
   
                875 ÷ 5 = 175 + R(0)
                175 ÷ 5 =   35 + R(0)
                  35 ÷ 5 =     7 + R(0)
                    7 ÷ 5 =     1 + R(2) 
                    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,
   
                  875 = 12000₅