Chapter 2 · Measurement and Problem Solving
2.6Problem Solving and Unit Conversion
12 min · two checks
Predict
How should a conversion factor be written so that kilometers become meters?
The idea
- Build a conversion factor from an equality.
- Solve a one-step unit conversion and check the size.
An equality such as 1 km = 1000 m can be written as a fraction equal to 1 in either direction. Multiplying by that fraction changes the unit and not the amount. Start from the given quantity, multiply by the factor whose denominator matches the unit you want to cancel, and stop when only the wanted unit remains. Then ask: should the number have gotten larger or smaller? Meters are smaller than kilometers, so a length in meters has a larger number. 2.4 km is 2400 m, not 0.0024 m.
A reliable path has four beats. Observe: copy the given number and unit, and the unit you want. Plan: write the equality. Compute: multiply and cancel. Check: significant figures from the measured value (defined factors are exact), plus a size check. Most “wrong” answers in this chapter are factors turned upside down.
Keep these
- A conversion factor is an equality written as a fraction equal to 1.
- The unwanted unit goes in the denominator so it cancels.
- If you move to a smaller unit, the number gets bigger.
Worked path
An aspirin tablet contains 325 mg of the active compound. Express that mass in grams.
Observe
Given 325 mg. Want grams. 325 has three significant figures.