Significant Figures: Zeros

Tutoring physics or chemistry, significant figures are part of the landscape.  Knowing when zero is significant can be tricky.

In this, our second installment on significant figures (see the first one here), we start on the practical question,  “What digits are significant?”  However, that question might be a bit ambitious for one post.  We’ll restrict today’s article to “When is zero significant?”

Numbers that result from calculations have other factors to consider.  For the purpose of this talk, we’ll assume we know nothing about how the number came about; we only know it “by sight”.

Case 1:  a zero between two nonzero digits.

Simple:  Always significant.

Example:  In the number 502, zero is significant.

Case 2:  a zero after a nonzero digit but before an unwritten decimal.

Simple:  Not significant.

Example:  In 7600 the zeros are not significant.

Case 3:  a zero after a nonzero digit, but before a written decimal.

Simple:  Always significant.

Example:  In 7600. the zeros are significant.

Yes, indeed:  120 and 120. are not the same, from a science point of view.  Their values are equal from the point of view of doing calculations, but the results of the calculations have different meaning.

Case 4:  Zeros to the left of the first nonzero digit.

Simple:  Never significant.

Example:  in 0.0035, the zeros are not significant.

Case 5:  Zeros following a nonzero digit and a decimal point:

Simple:  Always significant.

Example:  in 0.003 500 00, the four zeros following the five are significant.

Example:  in 13.0, the zero is significant.

We have another situation unique to significant figures:  12 and 12.0 are not the same.  80.1 and 80.100 are not the same, either, from the point of view of sig figs.

Let’s say you want a zero to be significant, but normal rules say it’s not.  Consider the following number:

23 000

We know that, since the decimal is unwritten, the three zeros are not significant.  However, what if, from the measurement itself, you know that the first zero actually is significant?

You can put a dash over the 0 that normally wouldn’t be significant to show that it is:

Now that people use scientific notation (which we’ll need to discuss in a future post), you rarely see the dashes anymore.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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