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Dimensional Analysis: Converting Units & Ensuring Accuracy

Learn how to convert measurements using dimensional analysis, a mathematical process that guarantees accurate results. This unit covers conversion factors, creating a plan of attack, and practicing with various units.

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Dimensional Analysis: Converting Units & Ensuring Accuracy

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  1. Honors Chemistry Unit I - Power Point 9Dimensional Analysis Section 1.6 One way of assuring yourself that you are getting the CORRECT answer

  2. Dimensional Analysis Dimensional Analysis is the mathematical process of converting a given measurement to another unit. If you can multiply fractions, you can do Dimensional Analysis.

  3. Use dimensional analysis when converting a given result from one system of units to another. • To convert from one unit to another, use the equivalence statement that relates the two units. • Choose the appropriate conversion factor by looking at the direction of the required change (make sure the unwanted units cancel). • Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units. • Check that you have the correct number of sig figs. • Ask, does my answer make sense?

  4. Conversion Factors A conversion factor is an multiplier for converting a one set of units into another. 12 in = 1 ft 1 in = 2.54 cm 2.2 lbs = 1 kg 1 cm = 10-2 m 100 cm = 1 m Typically we display conversion factors as fractions. = OR OR OR OR OR

  5. Conversion Factors It helps to create a “Plan of Attack” with conversion factors to reach a desired unit. To do this the given unit (the unit you start with) is in the denominator and your desired unit (the unit you want) is in the numerator. Example… Convert ft → in 1ft x 12 in = 12 in 1ft

  6. Example #1 • A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? • To convert from one unit to another, use the equivalence statement that relates the two units. • 1 ft = 12 in • The two conversionfactors are:

  7. Example #1 • A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? • Derive the appropriate conversion factor by looking at the direction of the required change (to cancel the unwanted units). • Notice – start with what was given • Notice - the units in the numerator of the first term are in the denominator of the second term. This will always be the case.

  8. Example #1 • A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? • Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units. • Correct sig figs? Does my answer make sense?

  9. Dimensional Analysis More practice… Convert 15.5 ft → in Given measurement = 15.5 ft Plan: ft → in Conversion Factor: 15.5 ft x 12 in = 186 in 1 ft You try: Convert 23 in → cm Remember there are 2.54 cm in an inch Answer: 58.42 -> 58cm (2 sig figs)

  10. Conversion Factors Sometimes you will need multiple conversion factors to reach a desired unit. Example… Convert yds → m Plan: yds → ft → in → cm → m Example… Convert 75.0 yds → m 75.0 yds x 3 ft x 12 in x 2.54 cm x 1 m = 6,858 -> 6,860 m (3 sig figs) 1 yd 1 ft 1 in 100 cm

  11. Example #2 • An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams? • (1 kg = 2.2046 lbs; 1 kg = 1000 g) • Steps: • Begin with what was given (4.5 lbs) • Select appropriate conversion factor(s) so units cross off

  12. Example #3 A car is traveling at a rate of 65 miles per hour. How fast is the car traveling in km per sec? (1.61km = 1 mile) • Note we will solve it two ways – either way is fine • Here we began by converting hours to seconds • We used lines instead of parenthesis to help keep terms in the numerator and denominators separate. • Note – Here we began by converting miles to km = 65 miles 1 hour 1 min 60 sec 1 hour 60 min 1.61 km 1 mile = 0.029km/sec 1.61 km 1 mile 1 hour 60 min 1 min 60 sec 65 miles 1 hour 0.029km/sec

  13. Concept Check What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation. Sample Answer: Distance between New York and Los Angeles: 2500 miles Average gas mileage: 25 miles per gallon Average cost of gasoline: $3.25 per gallon

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