Ch 3.3 Dimensional Analysis First, let try the Ladder Method

KILO 1000 Units HECTO 100 Units DEKA 10 Units DECI 0.1 Unit CENTI 0.01 Unit MILLI Unit Meters Liters Grams Ladder Method How do you use the “ladder” method? 1 st – Determine your starting point. 2 nd – Count the “jumps” to your ending point. 3 rd – Move the decimal the same number of jumps in the same direction. 4 km = _________ m How many jumps does it take? Starting Point Ending Point 4. 1 __. 2 3 = 4000 m

Try these conversions using the ladder method mg = _______ g 1 L = _______ mL160 cm = _______ mm 14 km = _______ m109 g = _______ kg 250 m = _______ km Conversion Practice Compare using, or =. 56 cm 6 m 7 g 698 mg

Write the correct abbreviation for each metric unit. 1) Kilogram _____ 4) Milliliter _____ 7) Kilometer _____ 2) Meter _____ 5) Millimeter _____ 8) Centimeter _____ 3) Gram _____ 6) Liter _____ 9) Milligram _____ Try these conversions, using the ladder method. 10) 2000 mg = _______ g 15) 5 L = _______ mL 20) 16 cm = _______ mm 11) 104 km = _______ m 16) 198 g = _______ kg 21) 2500 m = _______ km 12) 480 cm = _____ m 17) 75 mL = _____ L 22) 65 g = _____ mg 13) 5.6 kg = _____ g 18) 50 cm = _____ m 23) 6.3 cm = _____ mm 14) 8 mm = _____ cm 19) 5.6 m = _____ cm 24) 120 mg = _____ g Metric Conversion Challenge

Metric Prefixes

m = 1 ___a) mm b) km c) dm g = 1 ___ a) mg b) kg c) dg L = 1 ___a) mL b) cL c) dL m = 1 ___ a) mm b) cm c) dm Learning Check

Units of Length ? kilometer (km) = 500 meters (m)? kilometer (km) = 500 meters (m) 2.5 meter (m) = ? centimeters (cm)2.5 meter (m) = ? centimeters (cm) 1 centimeter (cm) = ? millimeter (mm)1 centimeter (cm) = ? millimeter (mm) 1 nanometer (nm) = 1.0 x meter1 nanometer (nm) = 1.0 x meter O—H distance = 9.4 x m 9.4 x cm nm O—H distance = 9.4 x m 9.4 x cm nm

Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

Learning Check Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers

How many minutes are in 2.5 hours ? Conversion factor 2.5 hr x 60 min = 150 min 1 hr 1 hr cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

Sample Problem You have $7.25 in your pocket in quarters. How many quarters do you have?You have $7.25 in your pocket in quarters. How many quarters do you have? 7.25 dollars 4 quarters 1 dollar 1 dollar X = 29 quarters

You Try This One! If Jacob stands on Spencer’s shoulders, they are two and a half yards high. How many feet is that?

Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b)244 cm c)24.4 cm

Solution A rattlesnake is 2.44 m long. How long is the snake in cm? b)244 cm 2.44 m x 100 cm = 244 cm 1 m

Temperature Scales FahrenheitFahrenheit CelsiusCelsius KelvinKelvin Anders Celsius Lord Kelvin (William Thomson)

Temperature Scales 1 kelvin = 1 degree Celsius Notice that 1 kelvin = 1 degree Celsius Boiling point of water Freezing point of water Celsius 100 ˚C 0 ˚C 100˚C Kelvin 373 K 273 K 100 K Fahrenheit 32 ˚F 212 ˚F 180˚F

Calculations Using Temperature Generally require temp’s in kelvinsGenerally require temp’s in kelvins T (K) = t (˚C) T (K) = t (˚C) Body temp = 37 ˚C = 310 KBody temp = 37 ˚C = 310 K Liquid nitrogen = -196 ˚C = 77 KLiquid nitrogen = -196 ˚C = 77 K Generally require temp’s in kelvinsGenerally require temp’s in kelvins T (K) = t (˚C) T (K) = t (˚C) Body temp = 37 ˚C = 310 KBody temp = 37 ˚C = 310 K Liquid nitrogen = -196 ˚C = 77 KLiquid nitrogen = -196 ˚C = 77 K

Learning Check – Honors Only The normal temperature of a chickadee is 105.8°F. What is that temperature in °C? The normal temperature of a chickadee is 105.8°F. What is that temperature in °C? 1) 73.8 °C 2) 58.8 °C 3) 41.0 °C