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

Dan Heflin

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

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?????????

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.

Back to the question

• We were asked to find the point in the 19th place. So

• .1001001001001001001001001001001001001001001001001001001001001001

• So our answer is: 1