Converting from Base 10 to Base 3 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 685401 into Base 3.
  
Solution:
                                      
The given number which is 685401 is written in Base 10. 685401 can also be written as 685401₁₀. 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 3 number is a number whose digits are 0, 1 and 2. If you see a subscript of 3 at the given number, then that number is written in Base 3. Base 3 number is also called ternary system. 
      
Now, let's convert 685401 into Base 3. How? Let's divide 685401 by 3 as follows:
   
                685401 ÷ 3 = 228467 + R(0)
   
Next, let's divide the quotient, which is 228467, as follows: 
    
                685401 ÷ 3 = 228467 + R(0)
                228467 ÷ 3 =   76155 + R(2)
 
Do the same thing with 76155 until the quotient is 0 as follows:
   
                685401 ÷ 3 = 228467 + R(0)
                228467 ÷ 3 =   76155 + R(2)
                  76155 ÷ 3 =   25385 + R(0)
                  25385 ÷ 3 =     8461 + R(2)
                    8461 ÷ 3 =     2820 + R(1)
                    2820 ÷ 3 =       940 + R(0) 
                      940 ÷ 3 =       313 + R(1) 
                      313 ÷ 3 =       104 + R(1) 
                      104 ÷ 3 =         34 + R(2)  
                        34 ÷ 3 =         11 + R(1)  
                        11 ÷ 3 =           3 + R(2)  
                          3 ÷ 3 =           1 + R(0)  
                          1 ÷ 3 =           0 + R(1)  
                   
The remainders will be the digits of Base 3 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  685401 = 1021211012020₃ 
 

Converting from Base 10 to Base 3 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 951 into Base 3.
  
Solution:
                                      
The given number which is 951 is written in Base 10. 951 can also be written as 951₁₀. 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 3 number is a number whose digits are 0, 1 and 2. If you see a subscript of 3 at the given number, then that number is written in Base 3. Base 3 number is also called ternary system. 
      
Now, let's convert 951 into Base 3. How? Let's divide 951 by 3 as follows:
   
                951 ÷ 3 = 317 + R(0)
   
Next, let's divide the quotient, which is 317, as follows: 
    
                951 ÷ 3 = 317 + R(0)
                317 ÷ 3 = 105 + R(2)
 
Do the same thing with 105 until the quotient is 0 as follows:
   
                951 ÷ 3 = 317 + R(0)
                317 ÷ 3 = 105 + R(2)
                105 ÷ 3 =   35 + R(0)
                  35 ÷ 3 =   11 + R(2)
                  11 ÷ 3 =     3 + R(2)
                    3 ÷ 3 =     1 + R(0) 
                    1 ÷ 3 =     0 + R(1) 
                   
The remainders will be the digits of Base 3 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  951 = 1022020₃ 

Converting from Base 2 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 110111₂ into Base 10.
  
Solution:
                             
The given number which is 110111₂ is written in Base 2. Base 2 number is also called binary system. The digits of Base 2 number are 0, and 1.
   
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 110111₂ into Base 10. How? Let's multiply each digits by the powers of 2 as follows:
         
Base 2 Digits:        1      1      0      1      1      1
Multiply by:            2⁵     2⁴     2³    2²     2¹     2⁰
             
Add all the digits, we have
                 
(1 x 2⁵) + (1 x 2⁴) + (0 x 2³) + (1 x 2²) + (1 x 2¹) + (1 x 2⁰) = 32 + 16 + 0 + 4 + 2 + 1 = 55
             
Therefore, 110111₂ = 55

 

Converting from Base 2 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 101₂ into Base 10.
  
Solution:
                             
The given number which is 101₂ is written in Base 2. Base 2 number is also called binary system. The digits of Base 2 number are 0, and 1.
   
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 101₂ into Base 10. How? Let's multiply each digits by the powers of 2 as follows:

Base 2 Digits:        1      0      1
Multiply by:            2²     2¹     2⁰

Add all the digits, we have

(1 x 2²) + (0 x 2¹) + (1 x 2⁰) = 4 + 0 + 1 = 5

Therefore, 101₂ = 5

Converting from Base 10 to Base 2 Problems, 2

Category: Arithmetic

"Published in Newark, California, USA"

Convert 408 into Base 2.
  
Solution:
                        
The given number which is 408 is written in Base 10. 408 can also be written as 408₁₀. 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 2 number is a number whose digits are 0 and 1. If you see a subscript of 2 at the given number, then that number is written in Base 2. Base 2 number is also called binary system. 
      
Now, let's convert 408 into Base 2. How? Let's divide 408 by 2 as follows:
   
                408 ÷ 2 = 204 + R(0)
   
Next, let's divide the quotient, which is 204, as follows: 
    
                408 ÷ 2 = 204 + R(0)
                204 ÷ 2 = 102 + R(0)
 
Do the same thing with 102 until the quotient is 0 as follows:
   
                408 ÷ 2 = 204 + R(0)
                204 ÷ 2 = 102 + R(0)
                102 ÷ 2 =   51 + R(0)
                  51 ÷ 2 =   25 + R(1)
                  25 ÷ 2 =   12 + R(1)
                  12 ÷ 2 =     6 + R(0) 
                    6 ÷ 2 =     3 + R(0) 
                    3 ÷ 2 =     1 + R(1) 
                    1 ÷ 2 =     0 + R(1)  
   
The remainders will be the digits of Base 2 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  408 = 110011000₂ 
 

Converting from Base 10 to Base 2 Problems

Category: Arithmetic

"Published in Newark, California, USA"

Convert 85 into Base 2.

Solution:

The given number which is 85 is written in Base 10. 85 can also be written as 85₁₀. 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 2 number is a number whose digits are 0 and 1. If you see a subscript of 2 at the given number, then that number is written in Base 2. Base 2 number is also called binary system. 

Now, let's convert 85 into Base 2. How? Let's divide 85 by 2 as follows:

                85 ÷ 2 = 42 + R1

Next, let's divide the quotient, which is 42, as follows: 

                85 ÷ 2 = 42 + R(1)
                42 ÷ 2 = 21 + R(0)

Do the same thing with 21 until the quotient is 0 as follows:

                85 ÷ 2 = 42 + R(1)
                42 ÷ 2 = 21 + R(0)
                21 ÷ 2 = 10 + R(1)
                10 ÷ 2 =   5 + R(0)
                  5 ÷ 2 =   2 + R(1)
                  2 ÷ 2 =   1 + R(0) 
                  1 ÷ 2 =   0 + R(1) 

The remainders will be the digits of Base 2 number. Use the digits of the remainders from bottom to top. Therefore,

                  85 = 1010101₂ 

Roman to Hindu Arabic Numeral Problems, 5

Category: Arithmetic

"Published in Newark, California, USA"

Convert MMMDCLXXXMCCLXXV into its equivalent Hindu Arabic numeral.
      
Solution:
  
The given number,  MMMDCLXXXMCCLXXV is a Roman Numeral. In order to convert it into Hindu Arabic Numeral, you must memorize or remember the Roman Numerals Chart.
  
First, let's consider MMM. In Hindu Arabic numeral,  MMM is equivalent to 3,000,000. 3 is 1,000,000s digit.
  
Next, let's consider DC. In Hindu Arabic numeral, DC is equivalent to 600,000. 6 is 100,000s digit.

Next, let's consider LXXX. In Hindu Arabic numeral, LXXX is equivalent to 80,000. 8 is 10,000s digit.

Next, let's consider M. In Hindu Arabic numeral, M is equivalent to 1,000. 1 is 1,000s digit.  

  
Next, let's consider CC. In Hindu Arabic numeral, CC is equivalent to 200. 2 is 100s digit.

Next, let's consider LXX. In Hindu Arabic numeral, LXX is equivalent to 70. 7 is 10s digit.  
   
And lastly, consider V. In Hindu Arabic numeral, V is equivalent to 5. 5 is ones digit.
   
Therefore, MMMDCLXXXMCCLXXV  = 3,681,275.

Roman to Hindu Arabic Numeral Problems, 4

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert CDVMMMXCVIII into its equivalent Hindu Arabic numeral.
      
Solution:
  
The given number,  CDVMMMXCVIII is a Roman Numeral. In order to convert it into Hindu Arabic Numeral, you must memorize or remember the Roman Numerals Chart.
  
First, let's consider CD. In Hindu Arabic numeral,  CD is equivalent to 400,000. 4 is 100,000s digit.
  
Next, let's consider VMMM. In Hindu Arabic numeral, VMMM is equivalent to 8,000. 8 is 1,000s digit.
  
Next, let's consider XC. In Hindu Arabic numeral, XC is equivalent to 90. 9 is 10s digit.
   
And lastly, consider VIII. In Hindu Arabic numeral, VIII is equivalent to 8. 8 is ones digit.
   
Therefore, CDVMMMXCVIII  = 408,098.

Roman to Hindu Arabic Numeral Problems, 3

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert  LXMMMCCCIII into its equivalent Hindu Arabic numeral.
   
Solution:
  
The given number,  LXMMMCCCIII is a Roman Numeral. In order to convert it into Hindu Arabic Numeral, you must memorize or remember the Roman Numerals Chart.
  
First, let's consider LX. In Hindu Arabic numeral,  LX is equivalent to 60,000. 6 is 10,000s digit.
  
Next, let's consider MMM. In Hindu Arabic numeral, MMM is equivalent to 3,000. 3 is 1,000s digit.
  
Next, let's consider CCC. In Hindu Arabic numeral, CCC is equivalent to 300. 3 is 100s digit.
   
And lastly, consider III. In Hindu Arabic numeral, III is equivalent to 3. 3 is ones digit.
   
Therefore,  LXMMMCCCIII = 63,303.

Roman to Hindu Arabic Numeral Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert MVCDLXXIX into its equivalent Hindu Arabic numeral.
   
Solution:
  
The given number, MVCDLXXIX is a Roman Numeral. In order to convert it into Hindu Arabic Numeral, you must memorize or remember the Roman Numerals Chart.
  
First, let's consider MV. In Hindu Arabic numeral, MV is equivalent to 4,000. 4 is 1,000s digit.
  
Next, let's consider CD. In Hindu Arabic numeral, CD is equivalent to 400. 4 is 100s digit.

Next, let's consider LXX. In Hindu Arabic numeral, LXX is equivalent to 70. 7 is 10s digit.
   
And lastly, consider IX. In Hindu Arabic numeral, IX is equivalent to 9. 9 is ones digit.
   
Therefore, MVCDLXXIX = 4,479.

Roman to Hindu Arabic Numeral Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert CMLXXXVII into its equivalent Hindu Arabic numeral.

Solution:

The given number, CMLXXXVII is a Roman Numeral. In order to convert it into Hindu Arabic Numeral, you must memorize or remember the Roman Numerals Chart.

First, let's consider CM. In Hindu Arabic numeral, CM is equivalent to 900. 9 is 100s digit.

Next, let's consider LXXX. In Hindu Arabic numeral, LXXX is equivalent to 80. 8 is 10s digit.

And lastly, consider VII. In Hindu Arabic numeral, VII is equivalent to 7. 7 is ones digit.

Therefore, CMLXXXVII = 987.