Chapter 2 · Measurement and Problem Solving
2.8Unit Conversion in Both the Numerator and Denominator
12 min · two checks
Predict
A speed is 90.0 km/h. What has to happen to both the kilometers and the hours?
The idea
- Convert a derived unit such as km/h into m/s.
- Keep the fraction’s top and bottom under control.
Derived units are fractions. km/h means kilometers per one hour. You may convert the top to meters and the bottom to seconds in the same line. Nothing special is happening: each factor still equals 1, and you still cancel. People get lost when they convert only half of the unit and then treat the other half as decoration.
Write the starting quantity as a fraction, even if you were handed “90 kilometers an hour” in words. Multiply by (1000 m / 1 km) and by (1 h / 3600 s). Kilometers cancel, hours cancel, and m/s remains. Check the size: a highway speed near 90 km/h is about 25 m/s, a reasonable walking-of-a-car figure, not 25 km/s.
Keep these
- Convert numerator and denominator separately.
- Per means divided by. Write the fraction.
- Size-check speeds and densities; they are easy to mis-scale by 1000.
Worked path
Convert a speed of 18.0 m/s to km/h.
Observe
18.0 m/s has three significant figures. Want km/h.