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## Main Question or Discussion Point

I am trying to convert a mole quantity into a mass. ##m_{CO_2}## will represent mass, ##M_{CO_2}## will represent molar mass and ##n_{CO_2}## will represent mole quantity.

I have ##n_{CO_2} = 3.3## and ##M_{CO_2} = (12.01 + 2(16.00))##

So, ##m_{CO_2} = 3.3(12.01 + 2(16.00))##

If I compute the value of ##M_{CO_2}## first,

##m_{CO_2} = 3.3(44.01)## I don't have to round yet, since I am still only using significant figures.

I then complete my multiplication and due to 3.3 only having 2 significant figures, I get ##m_{CO_2} = 1.5 * 10^2##.

If I distribute in the following way:

##m_{CO_2} = 3.3(12.01) + 3.3(2)(16.00)##

I have to make sure each term only have 2 significant figures

##m_{CO_2} = 40 + 110 = 1.5 * 10^2##

My textbook suggest that I reduce rounding errors by grouping similar operations. Is one way better than the other?

I have ##n_{CO_2} = 3.3## and ##M_{CO_2} = (12.01 + 2(16.00))##

So, ##m_{CO_2} = 3.3(12.01 + 2(16.00))##

If I compute the value of ##M_{CO_2}## first,

##m_{CO_2} = 3.3(44.01)## I don't have to round yet, since I am still only using significant figures.

I then complete my multiplication and due to 3.3 only having 2 significant figures, I get ##m_{CO_2} = 1.5 * 10^2##.

If I distribute in the following way:

##m_{CO_2} = 3.3(12.01) + 3.3(2)(16.00)##

I have to make sure each term only have 2 significant figures

##m_{CO_2} = 40 + 110 = 1.5 * 10^2##

My textbook suggest that I reduce rounding errors by grouping similar operations. Is one way better than the other?