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In decimal I can discard zeros after the radix point, e.g.: $$ 0.250_{10} = 0.25_{10} $$ It seems to me that I can do the same with binary: $$ 0.10_2 = 0.1_2 $$ Because

$$ 1\times\frac{1}{2}+0\times\frac{1}{4} = 1\times\frac{1}{2} $$ Am I right?

Peeyush Kushwaha
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Max Koretskyi
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2 Answers2

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While Roberts Frost's answer is perfectly correct there is however one small catch!

When engaged in practical computations which seek to obtain an approximation $A$ to the solution $T$ of a complicated equation, then there is a profound difference between the statement $T \approx 1$ and the statement $T \approx 1.0$. In the first case, we implicitly state the error $E = T-A$ satisfies $|E| \leq 5\times10^{-1}$. In the second case, we implicitly make the stronger statement that $|E| \leq 5 \times 10^{-2}$.

By dropping the "extra" 0 we are selling ourselves short because we give the wrong impression of the quality of the approximation.

Carl Christian
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  • tl;dr no difference b/w 0.1 and 0.10 because of the base, but difference there is a difference in significant figures. (Though that's not something that the body of the question asks, but it's important to note given the current title) – Peeyush Kushwaha May 19 '16 at 15:13
  • @PeeyushKushwaha: Your edits are not visible to others until approved. I answered the question 60 minutes ago. I made an edit 54 minutes ago. You made an edit to the question which changed the title and became visible to all others 43 minutes ago. – Carl Christian May 19 '16 at 16:06
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    @PeeyushKushwaha: There is no decimal point in a binary number. It is called the binary point. In general we speak of the radix point. I would not have approved the new title. – Carl Christian May 19 '16 at 16:11
  • Oh. My bad. I'll edit it to say radix point – Peeyush Kushwaha May 20 '16 at 08:38
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Yes it's exactly the same system. The only restriction on decimal relative to binary is no digits 2-9. As per your proof, removing a trailing zero is always equivalent to subtracting zero and therefore has no effect.

it's a hire car baby
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