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Dimensional Analysis 101

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Dimensional Analysis 101

- Length – the distance between two points (m, cm, in, ft)
- Mass – the quantity of matter in an object (g, kg, lb, oz)
- Volume – a measure of space, in cubic units (m3, cm3, ft3, in3)
- Temperature – the degree of hotness or coldness of a body or environment (°F, °C, or K)

- 1 cm = 10 mm
- 1 m = 100 cm
- 1 m = 1000 mm
- 1 km = 1000 m
* The base unit (meters) can be changed to other units (grams, liters, etc). Prefixes remain the same (centi-, milli-, kilo-, etc.)

- Write down what you know, with units.
- Set up a “T-Chart.”
- Fill in the units of your conversion factor FIRST, making sure the given units cancel out.
- Add your key conversion factor into your T-chart.
- If necessary, continue steps 3 and 4 until you reach your desired answer.

- Write down what you know, with units.
- Set up a “T-Chart.”
- Fill in the units of your conversion factor FIRST, making sure the given units cancel out.
- Add your key conversion factor into your T-chart.
- If necessary, continue steps 3 and 4 until you reach your desired answer.

Convert 156 cm to m.

- 156 cm
- 156 cm
- 156 cmm
cm

- 156 cm1 m
100 cm

- = 1.56 m

Convert 98 m to km.

- 98 m
- 98 m
- 98 mkm
m

- 98 m1 km
1000 m

- = .098 km

Convert 1.74 m to mm.

- 1. 74 m
- 1.74 m
- 1.74 mmm
m

- 1.74 m1000 mm
1 m

- = 1740 mm

- Convert 2500 m to km.
- 3.54 m = _____ cm
- 30,000 km = _____ m
- Convert 45.3 cm to mm.
- Convert 14 mm to m.

- Convert 13077 mm to km.
- 13077 mm
- 13077 mm
- 13077 mmm
mm

- 13077 mmmkm
mmm

- 13077 mm1m1km
1000mm1000m

= .013077 km

BUT! We don’t have a conversion from mm to km! “Double” T-Chart!

To do the math: Multiply every across the top together. (13077 *1*1) . Do the same for the bottom (1000*1000). Divide these two numbers (13077/1,000,000)