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What is the most significant digit of

$$0.00234$$

I have a problem of figuring out where it is $0$ or $2$.

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5  
It's the leftmost non-zero digit. So $2$. –  Darth Geek Aug 21 at 8:54
    
@Babak S. I think in editing his post you may have removed one of the digits. –  Phonon Aug 21 at 9:04
    
@Phonon: As far as I remembered, I edited correctly because I just added some $. Sorry Zonik. Forgive me if I did it wrong. –  Babak S. Aug 21 at 9:06
    
@BabakS. it is no problem, don't worry, just wanted to be sure because as I was writing up the number changed :) –  Phonon Aug 21 at 9:07
6  
@Nick Little typo : $0.0023 = 2.3 \times 10^{\Large{-}3}$ :-) –  Thomas Produit Aug 21 at 9:56

1 Answer 1

up vote 15 down vote accepted

Leading zeros are never considered as significant digits, so here for $0.00234$ you have 3 significant digits, 2,3, and 4. The most significant one is 2 (first non-zero from left), because it has the greatest effect on the number (2/1000 has an order of magnitude 10 times larger than 3/10000 and so on...).

Another example: 3.14159

It has six significant digits (all of them give you useful information) and the most significant one is 3.

EDIT to add more detail: $0$s in $0.00234$ are called leading zeros, and such leading zeros are always insignificant. Whereas trailing zeros is the term used for zeros in e.g. $1.2300$ where there's a decimal part, and the zeros are important here as they impose the degree of precision (of measurements e.g.). Last but not least, zeros between significant digits are also considered significant, e.g. $503.103$, which has 6 significant digits.

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2  
I think you mean leading zeros. Trailing zeros can be significant, but there aren't any here. –  user2357112 Aug 21 at 10:44
    
@user2357112 well pointed out, yes indeed leading zeros is the right term to use for zeros in 0.00234 etc. I will add a small EDIT. –  Phonon Aug 21 at 11:58
    
If we need the leading zeros to be significant, can it be written in scientific notation as $0.0023 \times 10^0$? –  Stephen Schrauger Aug 21 at 15:05
2  
@StephenSchrauger. No. Leading zeros are never significant. That is not scientific notation. –  Jonas Meyer Aug 21 at 15:51

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