Re: [Science Olympiad Coaches] Clarification on Metric Mastery Measurement section

[Lauren Savage]

I'm not a Division B coach so I'm not terribly familiar with the rules of Metric Mastery, so take what I say with a grain of salt. But I am a HS Physics teacher and I teach sign figs to my students (Juniors and Seniors, many of whom are in or will take AP Chem or Physics). And I double checked this with my husband who is a precision engineer.

Sig figs communicate the degree of precision of the tool that is being used to measure. So if you give them a ruler with mm markings, then they shouldn't round to the nearest cm. If the true value of the length of this object is accepted to be 3.421cm, then using the ruler with mm increments, students should report 34.0mm. The 4 is the known digit in the mm place and the 0 is the estimated digit. An estimated digit can only be 0 or 5, you can say it's close to the marking or somewhere in between, but without further markings in between, you can't say with confidence that the next digit is a 1 vs a 2, etc.

If they are given a ruler with mm markings, you could ask them to report their answer in cm, but you would still need the same number of sig figs as if it were in mm. They should convert to cm, not round. So in the example above, this would be 3.40cm. Remember that 1mm=0.1cm.

On Mon, Mar 2, 2026, 9:41 PM R S <shahr...@gmail.com> wrote:

Hi,

I know it's a bit late in the game, but still asking for clarification:

The rule states:

Measurements must be made using the supervisor-supplied instruments, expressed to the instrument’s resolution (the smallest division/markings/graduations on its scale) plus one estimated digit (if appropriate/analog).

To receive points, measurements must be expressed using the proper resolution and estimated digit appropriate for the instrument(s) provided, and the proper unit of measurement.

The question is:

Let's say I've a ruler with cm, dm and mm markings on it. They ask you for the answer in cm. Let's say the ruler shows somewhere between 3 and 3.5 cm. How many significant digits should we put?

Do we put 4 sigfigs something like: 3.421 (because 2 represents mm marking on the ruler and 1 is the estimated digit)

Or do we put 3 sigfigs something like: 3.42 (4 represents dm and mm is the estimated digit)

Or do we put 2 sigfigs something like: 3.4 (4 dm is the estimated digit and that's it)

Any help in this regards, is greatly appreciated.

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[Kelly Bell]

Hi there.    Metric Mastery ES several times; MM coach from way back in 2012-13.    Great question.  Here's my take (and it agrees with the wise teacher who chimed in).  

Regardless of what unit they are asking for (centimeter, nanometer, gigameter!), identify the smallest unit on the analog tool in which ALL values are represented by a line.  On most classroom rulers, it's mm.  You'll want to estimate exactly one digit beyond mm.  So, that would be a 0.1 mm.   , Convert to whatever, keeping the same number of digits and precision - basically, just move the decimal point (or change the exponent if your kiddos are comfortable with scientific notation).

So, in your example, you say that the students are asking for how long the paperclip is in cm, and they are given your typical classroom ruler with a mark for every mm.  They line the left end of the paperclip with the zero of the paperclip and then read the length.  They see that the paperclip is between 3 and 4 cm.   They count the little lines between them and see that the paperclip is about 3.4 cm.   According to the event rules, they are to estimate exactly one digit beyond mm.  They think its closer to 3.4 cm than it is to 3.5 cm.   So, maybe 3.42 cm.  There's a good amount of wiggle room in the scoring, so they don't have to worry estimating it differently than the ES did when making the answer key.

If the station asked for the length in mm, it would be 34.2 mm.  If it asked for the length in m, it would be 0.0342 m.  Or, it's 0.0000342 km, 0.342 dm.   

Incorrect answers would include:

3.4 cm (one too few digits)

3.426 cm (one too many digits)

3.42 (if the unit is not provided on the answer sheet, you better write it down)

3.89 cm (correct number of digits, but estimate too far from actual, perhaps because student didn't line up the zero on ruler correctly).  

Bottom line:  You won't get any measurement points if you don't give the right precision when using an analog instrument for a direct measurement.   

I hope this helps.

Kelly

PS.   I think the rules are unclear on how to handle calculated values like area of triangle, volume of a cubic solid, density of a rock, etc.  They give one example in 4.d.iii (which is corrected on soinc) which appears to follow sig fig rules, though soinc's sig fig policy expressly states that Metric Mastery students are not responsible for sig figs.  So when I make answer keys, I give some leeway in number of digits by figuring out what is reasonable considering the tool used (and it could be two tools: a digital scale with a graduated cylinder for density).   So in the example given in the rules (student uses a typical ruler to get measurements to the 0.01 cm), a student finds two sides of a rectangle to be 13.45 cm and 22.32 cm.   The rules give this area to be "300.2 cm^2" which follows sig fig rules.  However, students punching these numbers into their calculators will get 300.204 cm^2.   I will allow 0.1 cm^2 to 0.001 cm^2 precision for that answer.   I want to allow answers that are sensible and mark wrong those that are insanely off target! 

[R S]

Thank you both for your responses. This was most certainly helpful