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Finding the 19th Digit Right of the Binary Point for (4/7) Conversion

This article explores the conversion of the fraction (4/7) into binary format, specifically focusing on determining the digit in the 19th place to the right of the binary point. The process begins with multiplying the fraction by 2, separating the whole number and the decimal part for repeated conversions. As we continue this conversion, we observe a repeating pattern in the binary representation: 100. We describe the step-by-step methodology to accurately identify the digits generated and conclude with the specific digit at the 19th position.

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Finding the 19th Digit Right of the Binary Point for (4/7) Conversion

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Presentation Transcript

  1. If is expressed in binary form, what is the digit in the 19 places to the right of the binary point? Dan Heflin

  2. Well, how do we do this? • You take the (4/7), and multiple by 2 to get 1.1428 • You take the whole number representation, which is 1 in this case. This number then becomes the first binary point to the right of the decimal. • So as of now, we have .1

  3. Continue this process • Well, before we continue, we must disregard the whole number in front. So, we have .1428, not 1.1428. • Then .1428 x 2 = 0.2856. So, we take the 0 and that is our next binary point. • So now, we have .10?????????

  4. Even more • So we continue to get 0.57142, so our number is now .100 • Then we get 1.1428, so now our number is .1001 • But wait! 1.1428 is the same number we started with! So this is a repeating decimal! • So our number is .1001001001001001001001001001001001001001001001001001001001001001 and so on.

  5. Back to the question • We were asked to find the point in the 19th place. So • .1001001001001001001001001001001001001001001001001001001001001001 • So our answer is: 1

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