Questions: Use the table, along with dimensional analysis, to convert the given unit to the unit indicated.
Volume in Cubic Units Capacity
1 cm^3 =1 mL
1 dm^3=1000 cm^3 =1 L
1 m^3 =1 kL
Transcript text: Use the table, along with dimensional analysis, to convert the given unit to the unit indicated.
\begin{tabular}{|ll|}
\hline Volume in Cubic Units & Capacity \\
\hline $1 \mathrm{~cm}^{3}$ & $=1 \mathrm{~mL}$ \\
\hline $1 \mathrm{dm}^{3}=1000 \mathrm{~cm}^{3}$ & $=1 \mathrm{~L}$ \\
\hline $1 \mathrm{~m}^{3}$ & $=1 \mathrm{~kL}$ \\
\hline
\end{tabular}
Solution
Solution Steps
Step 1: Identify the Initial and Target Units
The initial unit is cm^3, and the target unit is L.
Step 2: Refer to the Conversion Table
The conversion factor from cm^3 to L is 0.001.
Step 3: Apply Dimensional Analysis
By multiplying the initial volume 500 cm^3 by the conversion factor 0.001, we get 0.5 L.
Step 4: Round the Result
After rounding to 2 decimal places, the final volume is 0.5 L.
Final Answer:
The converted volume is 0.5 L after rounding to 2 decimal places.