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I am trying to convert 0.4 from base 10 to base 2. This is what I did:

0.4 * 2 = 0.8 
0.8 * 2 = 1.6
0.6 * 2 = 1.2
0.2 * 2 = 0.4
0.4 * 2 = 0.8
0.8 * 2 = 1.6

Because 0.8 and 1.6 are repeated, I stop right here, and "0110" is what I got. But, 0.0110 is 0.375 in base 2, not 0.4. So obviously, I did something wrong, can anyone point out where the error is?

Rogan Farrira
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1 Answers1

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Here they say, that once it's started to repeat itself, it means, that it's just a recurring fraction. So I believe, 0.410 = 0.(0110)2 meaning that 0110 -part is recurring, it goes 0.011001100110...

dmk
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  • So, 0.4 is not recurring on base 10, but is recurring on base 2? When you say recurring, do you mean the same thing as "1/3" in decimal form, which is 0.3333333.... – Rogan Farrira Feb 01 '18 at 06:48
  • Yeah, as far as I know, fraction can be recurring in one base and not-recurrent in another – dmk Feb 05 '18 at 09:42