Section 1.3 Metric and Unit Conversions Metric Conversions The Ladder Method 1 Ladder Method 2 KILO 3 1000 HECTO Units 100 DEKA Units 10 Units DECI 0.1 CENTI Unit 0.01 MILLI Meters Unit 0.001 Liters Unit Grams How do you use the “ladder” method? 4 km = _________ m 1st – Determine your starting point. Starting Point Ending Point 2nd – Count the “jumps” to your ending point. How many jumps does it take? 3rd – Move the decimal the same number of jumps in the same direction. 4. __. __. __. = 4000 m 1 2 3 Conversion Practice Try these conversions using the ladder method: 1000 mg = _______1 g 1 L = _______1,000 mL 160 cm = _______1,600 mm 14 km = _______14,000 m 109 g = _______.109 kg 250 m = _______.250 km Conversion of Squared Units 1 cm2 = _____ mm2 1 cm x 1 cm = ____ mm2 (Convert 1cm to mm) 10mm x 10mm = 100 mm2 1 m2 = ___ cm2 1m x 1m = ______ cm2 (Convert 1m to cm) 100 cm x 100 cm = 10,000 cm2 6 m2 = ____ mm2 6 x 1 m x 1 m = ____ mm2 (Convert 1m to mm) 6 x 1,000 mm x 1,000 mm = 6,000,000 mm2 4 cm2 = _____ mm2 4 x 1 cm x 1 cm = ____ mm2 (Convert 1cm to mm) 4 x 10 mm x 10 mm = 400 mm2 Dimensional Analysis / Conversions • The fundamental or base quantities, such as length, mass, and time are called dimensions. • Dimensional Analysis is a procedure by which the dimensional correctness of an equation can be checked. • Both sides of an equation must not only be equal in numerical value, but also in dimension. • Dimensions can be treated like algebraic quantities. Dimensional Analysis / Conversion • Units, instead of dimensional symbols, may be used in unit analysis. • Used in chemistry, physics, engineering, and medicine • This is different than a math class – this is science!! • The units mean something • Simple unit conversions; the idea of dimensional analysis • We need a conversion factor, a relationship between the units (This MUST be shown in all conversions!!!) Dimensional Analysis/ Conversions Two Important Things: 1. The units on the given problem 2. The correct conversion factor(s) for the given units Conversion Factor = Fraction = Ratio } 1 inch = 2.54 cm can be written as a fraction } Either side can go on top } 1 in / 2.54 cm } 2.54 cm / 1 in Dimensional Analysis/ Conversions NOTE: You do not have to show conversions using the ladder method if the base units remain the same. Example: 100 cm = 1 m Notice the base unit is still in meters, we are just using a different prefix. Conversions – Single Step Step #1: Write the given. Step #2: Draw a chart (if necessary) Step #3: What is your conversion relationship? Step #4: Cancel units diagonally Conversions – Single Step Example #1 Calculate the number of minutes in 3.61 hours. Step #1: Write the given. Step #2: Draw the chart (If necessary) Conversions – Single Step Example #1 Calculate the number of minutes in 3.61 hours. Step #3: What is your conversion relationship? Step #4: Cancel units diagonally Conversions – Single Step Example #1 Calculate the number of minutes in 3.61 hours. Step #5: Multiply the top numbers together Step #6: Multiply the bottom number together Step #7: Divide Conversions – Single Step Example #2 How many centimeters are in 4.2 inches? 10.67 cm Conversions: Multi-Steps Example #3 Calculate the number of seconds in 2 weeks ü Realize that we don’t know just one conversion (step) from weeks to seconds. ü Start as Usual!!! ü Keep extending your table and adding conversion relationships as needed!! Conversions: Multi-Steps Example #3 Calculate the number of seconds in 2 weeks 1,209,600 sec Conversions: Multi-Steps Example #4 Convert 5 days to hours 120 Hours Example #5 How many seconds are there in 4 minutes? 240 Seconds Conversions: Multi-Units Example #6 Convert 50 m/s to km/hr? 50m 1km 3600s x x = 180 km/h s 1000m 1hr Starting Conversion Conversion Result Value Factor for Factor for Meters seconds Conversions: Multi-Units Example #7 Convert 147 ft/s to miles/hr 100.23 mi/hr Conversions: Multi-Units Example #8 Convert 60 m/s to ft/s 196.85 ft/s Conversions: Multi-Units Example #9 Convert 120 km/hr to ft/s 109.36 ft/s Conversions: Multi-Units Example #10 Convert 25 m/s to km/hr 90 km/hr Conversions: Multi-Units Example #11 Convert 75 km/hr to m/s 20.83 m/s .