2.6 – NOTES Dimensional Analysis

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Presentation transcript:

2.6 – NOTES Dimensional Analysis

Dimensional Analysis (Factor-Label Method) 1. Conversion factor – An equality such as “12inches = 1 foot”. If this conversion factor is expressed as a fraction, then it has the value of 1: 1 foot = 1 12 inches Multiplying a quantity by 1 does not change the value of the quantity. If the conversion factor is exact (1cm3 = 1mL) it will not affect significance. 2. Definition – An approach to changing units making use of conversion factors.

Dimensional Analysis (Factor-Label Method) HELPFUL HINTS: When solving these problems, use the conversion factors given as a means to convert units. The unit you are trying to eliminate should always go on the opposite side. Always start with your given. If you set up the conversion factor first, with units on opposite sides, and then put in the numbers, should lead to the correct answer

Sample problems: 1. A distance of 320. inches is equal to how many feet? 320. in x 1 ft = 26.7 ft 12 in ** The answer has 3 sig figs because the given had 3 sig figs.

Sample problems: 2. 17.4 hours is equal to how many minutes? 17.4 hours x 60 min = 1044 min = 1040 min 1 hr ** The answer has 3 sig figs because the given had 3 sig figs

Sample problems: 3.1,480,000 inches are equal to how many miles? = 23.4 mL

3. English to metric conversion factors Learn these: 1. 1 cm3 = 1 mL (exact) 2. 1 L = 1.06 qt 3. 1 lb = 453.6 g 4. 1 kg = 2.20 lb 5. 1 inch = 2.54 cm (exact) 6. 1 m = 39.37 in 7. 1 mile = 1.609 km 8. 1 hour = 3600 sec *Unless indicated otherwise, these conversion factors are rounded to 3 or 4 significant figures.