SOLUTION: 1. Convert the binary number 111,000,111 into the base ten equivalent. 2. Convert the base ten number 111 into the binary equivalent. 3. Convert the decimal number 0.35743574

Algebra ->  Decimal-numbers -> SOLUTION: 1. Convert the binary number 111,000,111 into the base ten equivalent. 2. Convert the base ten number 111 into the binary equivalent. 3. Convert the decimal number 0.35743574      Log On


   

Question 545299: 1. Convert the binary number 111,000,111 into the base ten equivalent.
2. Convert the base ten number 111 into the binary equivalent.
3. Convert the decimal number 0.35743574357435743574357435743574 to a fraction
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
1. Convert the binary number 111000111 into the base ten equivalent.
 1     1      1      0     0      0      1     1      1 

1*28 + 1*27 + 1*26 + 0*25 + 0*24 + 0*23 + 1*22 + 1*21 + 1*20
 258 +  128 +  64  + 0  +  0  +   0  +   4  +  2   +  1   = 457

2. Convert the base ten number 111 into the binary equivalent.

Keep dividing by 2 putting the quotients underneath and the
remainder out to the right beside the quotient.  Quit when
the quotient becoms 0.  Then the digits of the binary number
are the remainders reading from bottom to top:

   2)111
    2)55  1
    2)27  1
    2)13  1
     2)6  0
     2)3  1
     2)1  1
       0  1    
   
List the remainders from bottom to top

Answer:  1110111 


3. Convert the decimal number 0.35743574357435743574357435743574...
   to a fraction

       N = 0.35743574357435743574357435743574...

There are four repeating digits so multiply both sides by 104 or 10000

 10000N = 3574.3574357435743574357435743574...

Subtract the original equation for N

 10000N = 3574.35743574357435743574357435743574...
      N =    0.35743574357435743574357435743574...
--------------------------------------------------
  9999N = 3574

      N = 3574%2F9999  It doesn't reduce.   


Edwin