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Dimensional Analysis 101. Measurements and Units. 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 (m 3 , cm 3 , ft 3 , in 3 )

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measurements and units
Measurements and Units
  • 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)
key metric conversion factors
Key Metric Conversion Factors
  • 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.)

dimensional analysis steps
Dimensional Analysis Steps
  • 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.
example 1
Example 1
  • 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 cm m

cm

  • 156 cm 1 m

100 cm

  • = 1.56 m
more practice
More Practice

Convert 98 m to km.

  • 98 m
  • 98 m
  • 98 m km

m

  • 98 m 1 km

1000 m

  • = .098 km

Convert 1.74 m to mm.

  • 1. 74 m
  • 1.74 m
  • 1.74 m mm

m

  • 1.74 m 1000 mm

1 m

  • = 1740 mm
your turn
Your turn
  • Convert 2500 m to km.
  • 3.54 m = _____ cm
  • 30,000 km = _____ m
  • Convert 45.3 cm to mm.
  • Convert 14 mm to m.
multiple step problems
Multiple Step Problems
  • Convert 13077 mm to km.
  • 13077 mm
  • 13077 mm
  • 13077 mm m

mm

  • 13077 mm m km

mm m

  • 13077 mm 1 m 1 km

1000 mm 1000 m

= .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)

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