Sig Fig question - addition and subtraction

I got a question via email:
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Would you help me with the question in the textbook, p.40, Example 1.4 (b)?

1. 4 (b) Subtract 421.23 g from 486 g.

I thought 486's sig fig is 3 and 421.23's is 5. Doesn't the answer have to coincide with the fewest decimal places? The answer was 64.77 so I rounded it up to 64.8, and its sig fig is 3. I don't understand why the correct answer is 65g, its sig fig is 2 then.

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Significant figures are something that takes practice, so let's walk through this one step by step. Before we get too tied up in the math, remember that the whole reason we evaluate significant figures is to help us see where the uncertainty is in a number that we report.

First, let's just "do the math" given in the question... that's the simple part.

486g - 421.23g = 64.77g

Now we get to the more critical part... evaluating the information that we are using to get that answer. For addition and subtraction, we round the result of the addition or subtraction to the least-precise decimal place from the inputs. The "least precise" decimal place tells us where the uncertainty starts.

486g (in this case) really means that the true value is less than 487g but greater than 485g. That's the uncertainty we are trying to keep track of with significant figures. Similarly, 421.23g is really less than 421.24g but greater than 421.22g. When we subtract these values, we round to the "ones" digit because that is the least-precise input.

It's not that unusual to gain or lose sig figs when using the addition & subtraction rules. When adding and subtracting, don't worry as much about counting sig figs, just make sure you're rounding to the correct position in your result. 6.3 and 5.9 each have 2 sig figs, but when you add them together, the result (12.2) has 3 sig figs because we round to the least precise position, in this case the tenths place.

When multiplying and dividing, that's when we count the sig figs. Count the sig figs of the inputs and round the result to the same number of sig figs as the input with the fewest sig figs.