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