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## Main Question or Discussion Point

I came across a significant figures problem today that I need information on. The problem is this: "What volume of water can a cylindrical container hold of it is 13.0 cm tall and 12.0 cm in diameter? Show your work and express the answer in scientific notation using significant figures."

Of course the volume formula requires radius. When the radius is calculated, the precision allows estimation of 0.1 cm. Because of this, the radius (as I understand it) would have to be recorded as 6.0 cm.

It is evident that one significant figure is lost from the original measurement although it can be seen that the original 12.0 cm has three significant figures. When the final calculation is done, the answer is limited to two significant figures because significant figures must be determined after each step in the process. (The reduction in significant figures was precipitated by division by an exact number, not a measured value with only two significant figures.)

Is my understanding of this correct, and if so, isn't the precision of the final answer artificially reduced from what in real life could be observed?

Of course the volume formula requires radius. When the radius is calculated, the precision allows estimation of 0.1 cm. Because of this, the radius (as I understand it) would have to be recorded as 6.0 cm.

It is evident that one significant figure is lost from the original measurement although it can be seen that the original 12.0 cm has three significant figures. When the final calculation is done, the answer is limited to two significant figures because significant figures must be determined after each step in the process. (The reduction in significant figures was precipitated by division by an exact number, not a measured value with only two significant figures.)

Is my understanding of this correct, and if so, isn't the precision of the final answer artificially reduced from what in real life could be observed?

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