What does it mean to calculate "weight of SiO2 in the form of Si"?

This is with reference to the typical mass balance problems in iron making. Whenever we are asked to mole balance $\ce{SiO\_2}$ it is treated this way:


$W\_{\ce{SiO\_2}}$ from iron ore + $W\_{\ce{SiO\_2}}$ from coke = **$W\_{\ce{SiO\_2}}$ in the form of $W\_{\ce{Si}}$** in hot metal+$W\_{\ce{SiO\_2}}$ in slag.


Please explain the meaning of the highlighted part. What is the meaning of **"weight in the form of"**?




When the silicon in $\ce{SiO2}$ is converted it of course ceases to be present as $\ce{SiO2}$, but you can "pretend" that it still is. It is algebraically simpler to compute a weight of $\ce{SiO2}$, equivalent to the reduced weight $W\_{\ce{Si}}$. All you have to do is subtract the remaining weight of $\ce{SiO2}$ from the starting amount. This is a bit simpler then to report $W\_{\ce{Si}}$, since the latter calculation requires conversions using molecular and atomic weights for $\ce{SiO2}$ and $\ce{Si}$, respectively. 


It also makes it particularly easy to compute a quantity like %yield as follows: 


$ \% yield = 100 \times W\_{\ce{SiO\_2}}$ in the form of $W\_{\ce{Si}}$ in hot metal/$(W\_{\ce{SiO\_2}}$from iron ore+ $W\_{\ce{SiO\_2}}$ from coke)


Here %yield refers to the molar yield of reduced Si relative to total starting amount of Si.


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