Dimensional analysis 101
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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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Dimensional Analysis 101

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Dimensional analysis 101

Dimensional Analysis 101


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 cmm

    cm

  • 156 cm1 m

    100 cm

  • = 1.56 m


More practice

More Practice

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


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 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)


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