Chapter 2 · Measurement and Problem Solving
2.7Solving Multistep Unit Conversion Problems
12 min · two checks
Predict
If you cannot convert directly, what do you put in the middle of the path?
The idea
- Chain conversion factors without dropping units.
- Choose an intermediate unit on purpose.
Many equalities do not jump straight from the unit you have to the unit you want. You build a chain. To go from hours to seconds you may pass through minutes, or you may know 1 h = 3600 s. Both are fine if each factor equals 1. Write the factors in a single line so you can see every cancellation before you multiply the numbers.
Pick the intermediate unit that you can defend. Kilometers to centimeters is painless through meters: km → m → cm. Inverted factors are easier to spot in a chain than in your head, because a unit that refuses to cancel is still sitting on the page. At the end, significant figures follow the measured quantity, not the defined metric factors.
Keep these
- Stack factors; cancel units before you calculate.
- A stubborn unit means a factor is inverted or missing.
- Defined metric links (km, m, cm) are exact.
Worked path
A reaction runs for 2.75 hours. How many seconds is that?
Observe
Given 2.75 h, three significant figures. Want seconds.