Chemistry / Unit 1: Matter and Measurement
1.7 Dimensional Analysis
Notes
Dimensional analysis converts units by multiplying by conversion factors, fractions equal to 1 such as $\displaystyle \frac{1000 \text{ m}}{1 \text{ km}}$.
- Set up each factor so the unit you want to remove is on the bottom and cancels.
- Chain factors for multi-step conversions.
- Example: $\displaystyle 72 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} = 20 \text{ m/s}$.
- Check: the units should cancel to the units you want.
Practice
Convert 2.5 km to meters.
$\displaystyle 2.5 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} = 2500$ m.
How many milliliters are in 0.350 L?
$\displaystyle 0.350 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}} = 350$ mL.
A runner covers 1500 m in 5.0 minutes. What is the speed in m/s?
$\displaystyle 5.0 \text{ min} \times \frac{60 \text{ s}}{1 \text{ min}} = 300$ s, and $\displaystyle \frac{1500}{300} = 5.0$ m/s.
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