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Factor-Label Method • Based on Conversion factors, which are relationships between the units. • A conversion factor is used to convert a unit to any other related unit. • The conversion factor is derived from the equivalence statement of the two units. For example: 1 inch = 2.54 cm. • It is a ratio equivalent to 1 ALWAYS WORK THROUGH THE BASE UNITS!!!!!!! • Example: 1 m = 100 cm 1m 100 cm 1m 100 cm 1m 100 cm = 100 cm 1m 100 cm 1m 1 = = 1 Conversion factors = 100 cm = 1m 100 cm = 1m 100 cm • The correct choice is the one that allows the cancellation of the unwanted units. 1m Problem Solving Strategies: • • • • 1. 2. 3. 4. Write the known value (given) Draw the baseline (cross) Write the wanted units (units of the answer) Write the necessary conversion factors • If the unit to be eliminated is in the numerator of the given information then that unit should appear in the denominator of the conversion factor, and vice versa. Example: • • • • How many milligrams are in 2 micrograms? Step 1: Write the given. Step 2: Draw the baseline Step 3: Write the wanted units (units of the answer) Step 4: Write the conversion factor(s). SINCE I DO NOT KNOW A DIRECT RELATIONSHIP, I WORK THROUGH THE BASE UNIT 2 g 1g 1000 mg 1 000 000 g 1g = 0.002 mg Example: Given: 60 km/hr Want: cm/s 60 60 60km km km 1000 1000 1000m m m 100 100 cm cm 1 hr 11min min 111hr hr hr 111km km km 11 m m 60 min 60 60ss = == 1666.67 cm/s cm/s cm/s Example: You are driving 65 mph and take your eyes off the road for “Just a Second.” How many feet do you travel in this time? 1s 1 min 60 s 1 hour 65 miles 60 min 1 hour 65 miles or 1 hour 5280 ft 1 hour = 1 mile 65 miles 95.333 feet 1 inch = 2.20 lb = • • • • • • 2.54 cm 1 kg Convert the following quantities from one unit to another 30 m to mi 1500 yd to mi 206 mi to m 34 kg to lbs 34 lb to kg 20630 mim 5280 100 1500 feet cmyd 34 kg lb 12 1 inch inch 3 feet2.2o 1 kg 2.54 1lbs foot 1 cm mile 1 mile 1m = = 15.4545 74.8 0.85227 = lbs =0.018641 kg miles 331524.864 miles m 1mi 1m 2.54 1 foot 1cm yd2.2o 1 kg 121lbs 5280 inch inch feet5280 100feet cm In the lab we need to determine the reliability of our measurements 2 ways • Accuracy - how close is a measurement to the true or correct value for the quantity. ▫ Percent error • Precision - how close a set of measurements for a quantity are to one another, regardless of whether the measurements are correct. ▫ Significant digits Accurate or Precise?!?!? PRECISION ACCURACY Reproducibility Correctness Check by repeating measurements Check by using a different method Poor accuracy results from Poor precision results from procedural or equipment poor technique flaws Significant digits Percent Error Consider the three sets of data below that have been recorded after measuring a piece of wire that was exactly 6.000 cm long. SET X 5.864 cm 5.878 cm SET Y 6.002 cm 6.004 cm SET Z 5.872 cm 5.868 cm •Which set of data is the most accurate? •Which set of data is the most precise? •Which set of data is more precise, set X or set Z? Precise or Accurate?!?!? • A nickel has a mass of 5.0 g. • You measure it 4 times: 1. 1.05 g 2. 10.13 g 3. 6.28 g 4. 0.92 g 1. 2. 3. 4. 10.62 g 10.70 g 10.69 g 10.65 g 1. 2. 3. 4. 4.91 g 5.00 g 5.09 g 4.99 g