Sure, let's work through the conversion step by step to fill in the missing part of the equation.
Given:
[tex]\[
\left(-8.9 \times 10^4 \frac{ g }{ cm^3}\right)
\][/tex]
We're converting from [tex]\( \frac{g}{cm^3} \)[/tex] to [tex]\( \frac{g}{m^3} \)[/tex].
To do this, we need to know the conversion factor between [tex]\( \text{cm}^3 \)[/tex] and [tex]\( \text{m}^3 \)[/tex].
1 [tex]\( m^3 \)[/tex] is equal to [tex]\( 10^6 cm^3 \)[/tex]. Therefore, our conversion factor is [tex]\( 10^6 \)[/tex]:
[tex]\[
1 \text{ m}^3 = 10^6 \text{ cm}^3
\][/tex]
We multiply the given value by the conversion factor to perform the conversion:
[tex]\[
\left(-8.9 \times 10^4 \frac{ g }{ cm^3}\right) \cdot \left(10^6 \frac{ cm^3 }{ m^3}\right)
\][/tex]
Now, let's calculate the result:
[tex]\[
(-8.9 \times 10^4) \times 10^6 = -8.9 \times 10^{10}
\][/tex]
So, the missing part of the equation should be [tex]\( 10^6 \)[/tex]:
[tex]\[
\left(-8.9 \times 10^4 \frac{ g }{ cm^3}\right) \cdot 10^6 = -8.9 \times 10^{10} \frac{ g }{ m^3}
\][/tex]
Thus, the student's final equation is:
[tex]\[
\left(-8.9 \times 10^4 \frac{ g }{ cm^3}\right) \cdot 10^6 = -8.9 \times 10^{10} \frac{ g }{ m^3}
\][/tex]
