1. Conversion factors and units February 2012

2. Conversion Factors • In Scienceitisfrequentlynecessarytodealwithquantitieswhoseunits are nothomogeneous. • Youcannotaddkilometersto miles, orpoundstokilograms, as anexample. • Toensurecorrectcalculations, alltheunitsneedtobeconverted so thatthey are compatible. • In ourglobalizedeconomiesconvertingunitsbecomes a real necessity.

3. Conversion Factors • To convert a quantity to different units you need to multiply the original quantity by an appropriate conversion factor. • Conversion factors are ratios in which both the numerator and denominator represent equivalent quantities but are expressed in different units. • Because any quantity divided by itself equals to 1, all conversion factors are equal to 1. Therefore, when you multiply times the conversion factor, you end up with a different number and units, but equivalent to the original quantity.

4. How to convert • Step 1: Look at your original units, and determine the units you want to have. • Step 2: Find the conversion you need. The chosen factor will have both the original units and the desired units. • Step 3: Tomaketheconversiontakethe original quantity and multiplybytheappropriate factor, tomakesurethattheunwantedunitswillgetsimplified. • The conversion factor should have equivalent quantities both in numerator and denominator.

5. Example: Convert 0,3 min to seconds • Step 1: 0,3 minutes to “X” seconds • Step 2: (60s/1min) • Step 3: 0,3 min (60s/1min) = 0,3min * 60s/1 min = 18s

6. Do not invert the conversion factor! • Be careful about which units to include in numerator and denominator of the conversion factor. • Your answer will be wrong if you invert the factor: • Step 1: 0,3 minutes to “X” seconds • Step 2: (1 min/60s) • Step 3: 0,3 min (1 min/60s) = 0,3min * 1min/60s = 0,005 min2/s • Notice that the units of the answer make no sense. Correct use of units lets you double check answer.

7. Unit Conversion • Conversion factor totransformhourstosecondsortheoppositeis: • 1 hour/3600 s or 3600s/1 hour • Example: Howmanysecondsdoesittaketowatch a typical 2 hourlongmovie?. • Ifweneed more thanoneconversionyou can apply as manyfactors as youneed. Do thesamemovieexercisebutconvertto minutes first, and thentoseconds.

8. Prefixes for Units of Measurement • Units can be converted multiplying by a ratio that equals one. For example, 1 m = 100 cm, then 1m/100cm = 1 • To convert 532 cm to meters: • 532 cm * (1m/100 cm) = 532m/100 = 5.32 m • The cm label is canceled because it appears in both the numerator and the denominator.

9. Problems • Convert 745 mm to meters: • The two units in this problem are millimeters and meters. The prefix “milli-” means 10-3 (1/1000). This means that in 1 mm there are 10-3 m. • Decide which conversion factor will give you the correct unit for the answer. The answer needs to be in meters. To get meters, use the conversion factor that multiplies by meters and divides by millimeters (to cancel millimeters in the number from the problem). • 745 mm * (1 m/1000mm) = 0,745 m

10. Problems • If a penny measures 19 mm (millimeters), how many kilometers does it measure? • Hint: there are 1000 mm in 1 m, and there are 1000 m in 1 km. You need to apply to conversion factors. • First, convert to meters, and then to kilometers.

11. Problems

12. Different units in different systems

13. Prefixes for Units of Measurement • Nano = 10-9= (1/109) • Micro = 10-6= (1/106) • Milli = 10-3= (1/103): 1000 millimeteres in 1 m • Centi = 10-2= (1/102): 100 cm in 1 m • Kilo = 103 : 1/1000 kilometers in 1 m, or 1000 m in 1 kilometer • Mega = 106 • Giga = 109

14. Unit Conversion – Practice • 1) How many minutes are there in 3,3 hours? • 2) How many seconds are there in 2,8 days? • 3) A rope is 8,56 m long. How long is the rope in cm? • 4) Convert 6 meters to inches. There are 2,54 cm per inch, and 100 cm per meter. One foot has 12 inches. • 5) If Peter’s height is 6 feet and 4 inches, what is his height in meters? (hint: there are 12 inches per feet, and 1 inch is equal to 2.54 cm).