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How to extract leading non-zero digit?

I'm working on a research problem related to Benford's Law which states that the distribution of leading digits is not random. This is probably because many things grow logarithmically. I am trying to extract the leading digit from these vectors below:
10 --> 1
13 --> 1
0.3 --> 3
-4 --> 4
-5 --> 5
-0.006 --> 6
Input will be a vector
x = [1 0.3 -2 0.001 -0.0006, 582398, 3020];
Output should be
y = [1 3 2 1 6 5 3];
Any help?

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4 Answers

Answer by Walter Roberson
on 20 Jan 2011
 Accepted Answer

The answer is complicated because numbers such as 0.0006 have no exact representation in binary floating point number, and the closest number that can be represented might not have the same leading binary digit.
If one does NOT take that factor in to account, then:
y = floor(abs(x) ./ 10.^floor(log10(abs(x))));

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I suggest to accept this one.
Sorry it took me so long to accept. I stole this question from Ned before Answers launched and forgot about it =).

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Answer by Ned Gulley on 11 Jan 2011

You'll probably need to do some kind of textual manipulation. Here's one way to do it.
function y = leadingDigit(x)
s = sprintf('%1.2e\n',abs(x));
y = s(1:(length(s)/length(x)):end)-48;
end

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Answer by Daniel Shub
on 28 Jun 2012

Is this really the first question on Answers? I was going to use our new magic power and start accepting answers. The only problem is I think there is now a better answer to this question on Loren's blog.

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I thought of accepting this answer, because it contains a link to good solutions. But actually the method shown by Walter hits the point (and is found in this blog also). Ned's method is more efficient than STR2DOUBLE, but a clean numerical approach is moire direct for a numerical question.

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Answer by Oleg Komarov on 5 Sep 2012

Another solution based on regexp (from this question):
regexp(num2str(x), '(?<=(^|\s+)[\-\.0]*)[1-9](?=[\d\.]*)', 'match')

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