Significant Figures addition & conversion

[physicsteach]

Having a discussion with a colleague over sig figs and conversions.

Original problem: find perimeter of 12.6 ft by 13.88 ft room and express answer in meters.

16.1 m or 16.2 m?

Question is when to round? After finding perimeter in feet? 53.0 feet to meters = 16.2 meters or at the end? 52.96 feet = 16.1 meters?

 

[daveb]

I find it's usually best to round at the final answer.

 

[SammyS]

I find it's usually best to round at the final answer.

(Emphatically) agree !

 

[Johnson]

Keep as many digits throughout your work as you can, then round at the end.

 

[rwisz]

As a scientist, it is important to pay attention to significant figures and conversions in order to accurately represent our data and findings. In this scenario, the original problem asks us to find the perimeter of a room in feet and then convert that answer to meters. When converting between units, it is important to maintain the same number of significant figures as the original measurement.

In this case, the perimeter is given as 12.6 ft and 13.88 ft. When adding these two measurements, we must be mindful of significant figures and round our answer accordingly. The rule for addition and subtraction is to round to the least number of decimal places in the original measurements. In this case, the original measurements have one and two decimal places respectively, so our final answer should also have one decimal place. Therefore, the perimeter of the room in feet would be 26.5 ft.

Next, we need to convert this answer to meters. The conversion factor for feet to meters is 0.3048. Multiplying our answer of 26.5 ft by this conversion factor gives us 8.0772 meters. Again, we must pay attention to significant figures and round our answer to the least number of decimal places in the original measurement. In this case, the original measurement had one decimal place, so our final answer should also have one decimal place. Therefore, the perimeter of the room in meters would be 8.1 m.

As for the question of when to round, it is important to round at each step of the calculation to maintain accuracy. In this case, we rounded after adding the two measurements in feet and then again after converting to meters. This ensures that our final answer is as precise as possible and reflects the accuracy of our original measurements.