Friday, February 24, 2006

Significant Figures and Scientific Notation

Why use scientific notation for small numbers like 8800?

How many significant figures do each of the following numbers have?

a) 2143

Four significant figures

b) 82.60

Four significant figures. The final zero in this number is not just a place holder, it is a part of the number.

c) 7.63

Three significant figures.

d) 0.03

One significant figure. The zeros in this number are merely placeholders. The number is better represented as 3x10-2.

e) 0.0085

Two significant figures.

f) 3336

Four significant figures.

g) 8800

This number is unclear. It might have two or four significant figures, depending on whether the zeros are a “real” part of the number or simply placeholders. If the number is only approximately 8800 (with the exact tens and units figures unknown), the number is properly written as 88x102 and has two significant figures. If, however, the number is known to be 8800 with uncertainty only in the tenths and smaller parts, then the number is correctly written and has four significant figures.

It is unfortunate that “normal” notation gives no way to distinguish between the two and four significant figure version of this number – a good reason to stick to scientific notation, which removes the ambiguity in these cases, even though 8800 is not so large that scientific notation is required to write it without a large string of zeros.

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