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Dimensional Analysis 101

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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  1. Dimensional Analysis 101

  2. 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)

  3. 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.)

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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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