October 26th, 2013, 08:24 AM  #1 
Senior Member Joined: Oct 2012 Posts: 460 Thanks: 0  0.1 binary
Hello! Please, as far as there are no problems to turn decimal numbers to binary, I just stuck at turning 0.1 to binary system. 0.1 : 2 = 0. rest 0.05 :2 = 0 rest 0.025 : 2 = o rest ... and the result should be infinite number containing 1s too: 0.00011001100110011 How do they get these 1s at all cause you can all the rational numbers divide with 2... Please, can someone help? Many thanks! 
October 26th, 2013, 09:13 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: 0.1 binary Hello, ungeheuer! Quote:
Here is one way . . . Assume that 0.1 (base ten) equals some decimal in base two. [color=beige]. . [/color] And we see that we have a repeating pattern. [color=beige]. . [/color]  
October 26th, 2013, 09:14 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs  Re: 0.1 binary In binary this is: Dividing by 2 moves the decimal point to the left one place, thus: 
October 26th, 2013, 09:33 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,114 Thanks: 1909 
Or use long division... Code: 0.000110011 __________________ 1010 1.0000000000 1010  1100 1010  10000 1010  1100 1010  etc. 

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