Significant figure question.

[lbergstrom]

I am helping to implement a chemistry class for some high schoolers and we have run into the problem about significant figures in the number 0.  As in 0°C.  In the problem below: Would 0°C in this situation be measured or exact. I assume measured but since it has no decimal then there would be no significant figures for it.  If that is the case and 0°C has no sig figs then do you move to the next lowest sig fig. OR does it have 1 sig fig?

Here is the example problem: 3. How many grams of chlorine gas (Cl2) are present in a 150. liter cylinder of chlorine held at a pressure of
1.00 atm and 0°C?

Here is the students work: 

[james783]

Hello,

You've hit upon a common point of confusion with significant figures! Let's break down why 0°C is considered measured in this context and how to handle it in calculations.

Understanding 0°C in the Problem:

Measured Value: In the given problem, 0°C represents a measured temperature. Even though it's a whole number, it was obtained using a thermometer or other temperature-measuring device. It's not a defined constant like the number of atoms in a molecule.  SunPass
Significance: The 0°C is not an exact number. It is a measurement that has been taken.
Significant Figures: 0°C in this context has one significant figure.
Why One Significant Figure?

The rule is that trailing zeros in a whole number without a decimal point are generally considered placeholders and not significant.
However, in context of measurement, the 0 indicates the precision of the measurement. If the temperature had been measured to a higher precision the value would have been something like 0.0°C or 0.00°C.
Therefore, the 0 is a significant figure because it represents the precision of the measurement.
Handling Significant Figures in Calculations:

When performing calculations with measured values, the result should be rounded to the least number of significant figures present in the original measurements.
In your example problem, you have:
liters (3 significant figures)
1.00 atm (3 significant figures)
0°C (1 significant figure)
Therefore, the final answer should be rounded to one significant figure.
Student's Work and Implications:

If the student's work involves using the ideal gas law (PV=nRT), they'll need to use the Kelvin temperature.
Converting 0°C to Kelvin: 0°C+273.15=273.15K.
When using 273.15K, it is important to remember that the 0°C measurement is the limiting factor in terms of significant figures. So the final answer should only have one significant figure.
When using the value 273.15K, the precision of the Kelvin conversion is higher than the original celcius measurement. However, the original measurement is the limiting factor.
If the student used 273K, they would be using the correct number of significant figures for this problem.
Key Takeaway:

Context is crucial when determining significant figures. 0°C in this problem is a measured value with one significant figure.
The final answer in calculations should be rounded to the least number of significant figures from the measured values.

Best Regards
james783