DIMENSIONAL ANALYSIS How many millimeters are in 1 foot?

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Presentation transcript:

DIMENSIONAL ANALYSIS How many millimeters are in 1 foot?

I You Some Questions

Metric vs English

What is Dimensional Analysis?  Converting from one unit to another.  Why do we want to do this?  When making scientific calculations, it is necessary for the numbers used to be dimensionally consistent. Consider Newton’s Second Law … a = F/m What is the unit label for acceleration? If Force is measured in kg * m/s 2, what units must mass be measured in?  If mass is given in pounds, the measurement must be converted to kilograms in order for the calculation to be dimensionally consistent.

Converting from One Unit to Another  Try converting lb to kg…  Use an equivalence statement that relates the two units.  1 kg = lb  Figure out the correct unit factor to use to cancel out the unwanted starting unit.  lbs  kg so …. lb(kg/lb) = kg  Multiply the starting number by the unit factor.  lb (1 kg/2.205 lb) = kg

Chemistry Vocabulary  An Equivalence Statement is a defined conversion factor between two different units. 1 foot = 12 inches 1 km = 1000 m1 mile = 1609 m  The units can be English to English, English to metric, metric to metric, or other.  Because these are defined, all numbers in the statement are infinitely significant.  Conversion Factors are ratios of the two parts of an equivalent. 1 foot = 1 = 12 inches 12 inches 1 foot

Dimensional Analysis  Dimensional Analysis is the algebraic conversion of one measurement unit to another using conversion factors.  Steps for converting from one unit to another: 1. Choose an equivalence statement that relates the two units. 2. Choose the appropriate conversion factor by looking at the direction of the required change. Make sure the unwanted units cancel out. ( Box Method) 3. Multiply the quantity to be converted by the conversion factor. 4. Check for the correct number of significant figures. 5. Check to see if the answer makes sense.