# Dimensional Analysis 101 - PowerPoint PPT Presentation

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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

### 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

• 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

• 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.

• If necessary, continue steps 3 and 4 until you reach your desired answer.

### 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.

• 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

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.

### 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)