Final answer:
Dimensional analysis is used to convert 1 cubic meter to liters by using the conversion factor that 1 m³ equals 1000 liters (1 x 10³ L), and setting up the conversion so cubic meters cancels out, leaving liters.
Step-by-step explanation:
The student asked how to apply dimensional analysis to convert 1m³ to liters. Dimensional analysis is a mathematical approach that uses conversion factors to switch from one unit of measurement to another. It’s based on the principle that units must undergo the same mathematical operations as their corresponding numbers.
In this case, we will use the conversion factor that 1 cubic meter (m³) equals 1000 liters (1 x 10³ L).
Let's perform dimensional analysis:
Start with the given information: 1 m³
Identify the conversion factor between cubic meters and liters: 1 m³ = 10³ liters
Set up the conversion so that the units cancel out:
1 m³ x (10³ liters / 1 m³) = 10³ liters
The unit of cubic meters (m³) cancels out, leaving the desired unit of liters. Therefore, 1 m³ is equal to 10³ or 1000 liters.