Student can use the unit factor method to convert between systems of measurement.
Explain how to multiply by fractions equal to 1 to cancel units.
Often while calculating, there is a need to convert units from one system to another. The method used to accomplish this is called the factor label method, unit factor method, or dimensional analysis.
Show how to convert L to m^3, emphasizing the cubing of the factor.
Problem. A jug contains of milk. Calculate the volume of the milk in .
Given:
Show how to chain multiple unit factors in one step.
Problem. How many seconds are there in 2 days?
A flowchart showing the chain of unit cancellations.
By chaining unit factors, you can convert across multiple systems in a single step by ensuring intermediate units cancel properly.
Arrange the unit factors to correctly convert a value.
Arrange the steps to correctly chain the conversion of 1 kilometer (km) into picometers (pm).
Solve Exercise 1.22 using dimensional analysis.
Problem: If the speed of light is , calculate the distance covered by light in .
List the known quantities and their units.
Provide the unit factor needed to convert nanoseconds (ns) to seconds (s).
Write out the full equation for distance (speed × time), including the unit factor to cancel ns.
Group the numerical parts and combine the exponents once the units are cancelled.
State the final numerical answer with correct units and significant figures.