From the submitter: “I came across these answers to sig fig questions when marking a pre-algebra numeracy test last night. I’ve attached two answers, one is a very common mistake where students just can’t believe that they are asked to round up that much. The second… well I don’t have any idea what the student was thinking, so I thought your readers might be able to help.”

• How can this be confusing? The first student—well, honestly, I wouldn’t even mark it wrong. That’s a really crappy trick to play on a kid. The second one just doesn’t quite understand what gets incremented.

• Why do you see this as a trick? It seems like a good question to assess whether a student has just memorized a simple ‘turn everything to 0’ type of algorithm or not. Seems like the payoff question here is a logical one. Second student? Wow – I’d need to sit down and ask some serious questions there.

• Dave

I’m usually the first person to jump on a bad problem, but I don’t take issue with this set. I don’t like it when a question is at all ambiguous or unclear. When the correct answer is very solidly obtainable but tricky or challenging, I’m OK with the problem. Just my two cents.

• Actually, I think the first one might be revealing. Are they rounding to 3 significant figures, or are they rounding to HAVE 3 TRAILING ZEROS? Given 12,842 would they give 12,800 or 13,000? Kind of an important distinction. There’s also the question of whether repeating the zero counts as a “single” significant digit, meaning we need to do something with the 5.

As to the second, I’m almost seeing the 3 Zero thing again in (b) and (c) – where they doubly rounded in (b) to have the number of zeroes at 3 – but (a) is kind of baffling. 970 and 120 don’t even add to 1000. (stares longer) Nope, no idea. Sorry.

• l hodge

I believe the second student may rounding different parts of the number separately. For b) & c) 28 & 46 are rounded to 30 & 50 respectively as a second phase of rounding. Part a) has me puzzled.

• OP

@Greg – The three trailing zero thing in the first picture is something that I didn’t notice – thanks for pointing that out. I’ll keep an eye out for that in the future.
As for the second picture – maybe they are trying to round substrings of numerals, but there’s nothing consistent in it.

• I think that might be it in the second one, but yeah, it’s not consistent. Like, in a, they get to a 9 and so round the one before it up, bringing the 9 down to 0. But then there’s a 6 after it, so that have to round that 0 up to 1, bringing the six down to 0. Then they’d round again, but I don’t know how they got 2. The idea definitely works for the second and third one, the only part that is out of place with that theory is the 2 near the end of a).

• The problem is incorrectly posed because there are spaces between the digits instead of the standard formatting with commas.

• OP

@CCSSIMath: Don’t be so provincial!
The “standard” is the SI conventions that uses spaces. See