My teacher said there are two ways to find the # of digits of a number but i dont get either of them
what does both of the codes mean?
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log 10 ( abs(n)) + 1
if n=0 d =1
else
d= log 10 ( abs(n))

the other one:
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absn= abs(n);
d= 1;
while ( abs(n) / 10 > 10 )
d++;
absn = absn /10;
}

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In the first one, he's using the fact that the base 10 logarithm of a number besides 0 is one less than its number of digits.
In the second one, he's seeing how many times he can divide the number by 10; this is its number of digits.
Try it out and see for yourself.
Edit: here's a simple Python snippet that demonstrates this:
http://ideone.com/iC8sPR
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