Significant Figures addition & conversion

AI Thread Summary
The discussion centers on the proper application of significant figures in conversions, specifically when calculating the perimeter of a room measuring 12.6 ft by 13.88 ft and converting the result to meters. Participants debate whether to round the intermediate value of 53.0 feet to meters as 16.2 meters or to use the more precise 52.96 feet, resulting in 16.1 meters. The consensus emphasizes the importance of retaining as many significant figures as possible throughout the calculations and rounding only at the final answer. This approach helps maintain accuracy in the final result. Rounding at the end is deemed the best practice for clarity and precision.
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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?
 
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I find it's usually best to round at the final answer.
 
daveb said:
I find it's usually best to round at the final answer.
(Emphatically) agree !
 
Keep as many digits throughout your work as you can, then round at the end.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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