Converting Units

Objectives:• 1. Write conversion factors from given unit

equalities.• 2. Explain how conversion factors are used in

dimensional analysis.• 3. Name and describe the four steps of problem

solving strategy.• 4. Explain why graphs are often used to display

experimental data.Key Terms:dimensional analysis, percent error, conversion factor

Dimensional Analysis• Dimensional analysis is the name given to the

process of converting units. Example: Convert the following to SI units. 75km/hr (Remember SI for length is the meter and SI for time is the second.) 75km x 1000m x h = 75000m = 20.8333m/s or 2.1x101m/s (2 significant digits) h x km x 3600s 3600s

• The above problem was solved taking advantage of conversion factors or what is called unit equalities. (1km = 1000m) Dimensional analysis is simply the method of organizing the unit equalities into an equation• Unit equalities are measurements with different units that

have the same value

Strategies for Solving Dimensional Analysis Problems• Always place your given amount (75km/h) on the left side of

the problem. • Place the unit equalities (1000m = 1km and 1h = 3600s) in

your equation so that the units that you don't want will cancel out.

• Make sure that the unit(s) of measure that you want to end with are still present and in the proper orientation before you solve. In the case of the problem above I wanted to end up with m/s. • Notice that I placed the meters and seconds in the appropriate

orientation for my desired answer.

• Solve the entire upper and lower portions of the equation. • Reduce the final amount and round to the appropriate

significant digits.

Graphing• Graphs are traditionally used to visually express

the relationship between two or more different but related quantities. The graph is constructed using the x-axis (horizontal) as the independent predictable reference and the y axis (vertical) as the dependent measured (responding) variable. You will notice in most graphs that the independent value (time) remains constant while the dependent value changes the shape and the meaning of the graph