Rounding
to a significant figure is when you have to round to "an appropriate
number of significant digits". What are significant digits? Well, they're
sort of the "interesting" or "important" digits. For
example,

3.14159
has six significant digits (all the numbers give you useful information)

1000
has one significant digit (only the 1 is interesting; you don't know anything
for sure about the hundreds, tens, or units places; the zeroes may just be
placeholders; they may have rounded something off to get this value)

1000.0
has five significant digits (the ".0" tells us something
interesting about the presumed accuracy of the measurement being made: that the
measurement is accurate to the tenths place, but that there happen to be zero
tenths)

0.00035
has two significant digits (only the 3 and 5 tell us something; the other
zeroes are placeholders, only providing information about relative size)

0.000350
has three significant digits (that last zero tells us that the measurement was made
accurate to that last digit, which just happened to have a value of zero)

1006
has four significant digits (the 1 and 6 are interesting, and we have to count
the zeroes, because they're between the two interesting numbers)

560
has two significant digits (the last zero is just a placeholder)

560.
(notice the "point" after the zero) has three significant digits (the
decimal point tells us that the measurement was made to the nearest unit, so
the zero is not just a placeholder)

560.0
has four significant digits (the zero in the tenths place means that the
measurement was made accurate to the tenths place, and that there just happen
to be zero tenths; the 5 and 6 give useful information, and the other zero is
between significant digits, and must therefore also be counted)

Sep 3rd, 2014

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