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Metric and dimensional analysis

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For conceptual physics students who have little math background

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  • 1. Kilo Hecto DekaUNITSGramLiterMeterUNITSdeci centi milliMetric to MetricMapUse it and you will never get lost!How To Use Your Map1) Start at the unit/prefix given to you (starting point).2) Count the number of steps/places to the unit/prefix you want (finaldestination)each is a factor of 10.3) Move the decimal point the number of steps/places in the samedirection.SMALLESTLARGEST

2. Kilo Hecto Deka Gram deci centi milliCheck for UnderstandingHow many mg are in 3.6 Kg?Starting point Final Destination3,600,000 mg6 places to the right of the decimal point 3. Kilo Hecto Deka Meter deci centi milliCheck for UnderstandingHow many hm are in 12.67 mm?Starting pointFinal Destination0.0001267 hm5 places to the left of the decimal point 4. Helpful MnemonicTry to create your own mnemonic to helpyou remember the prefixes and theirorder. This will be important because youwill not receive the metric map on yourquiz.Kings Have Diamonds BUT Diamonds Cost Money 5. 1. Read the question. The question will provide you with information thatidentifies your starting point and your final destination. Starting point = the number and unit provided by the question Final destination = the units desired after converting2. Write your starting point and your final destination.3. Determine how you will get from your starting point to your finaldestination (simply find connections or conversion factors betweenyour starting and final unit).Metric to US Conversion Steps(Dimensional Analysis) 6. Metric to US Conversion Steps(Dimensional Analysis)4. Create a fraction with your starting point.5. Write in the bottom unit of the new fraction. This should be the same as thetop unit of the previous fraction.6. Write one set of connections or conversion factors into the fraction. Yourbottom unit will guide you.7. Ask yourself, Do I have the desired unit (final destination) on the top of thenew fraction?NO YES8. Cancel any units that are diagonal. (This should leave you with only the unitsthat represent your final destination)9. Multiply the top of the fractionsmultiply the bottom of the fractionsdividethe top by the bottom.(Go back to step 5) (Proceed to step 8) 7. Practice Conversions1. How many seconds are in 6 minutes?360 seconds2. How many centimeters are in 27 inches?68.58 centimeters3. If a truck weighs 15,356 pounds, how many tons is it?7.678 tons4. If you had 10.5 gallons of milk, how many pints would youhave?84 pints5. Students go to school for 180 days. How many minutes is thisequal to?259,200 minutes 8. How many seconds are in 6 minutes?6 minutes seconds(6 minutes)1( )( )secondsminute360 seconds601=(6)(60 seconds)(1)(1)=Step 1 Read the question and determinewhat information it provides you with(starting point & final destination) Step 2 Write down yourstarting point and your finaldestination1 minute = 60 secondsStep 3 Determine howyou will getfrom yourstarting point toyour finaldestination (listanyconnections orconversionfactors)Step 4 Create a fractionwith your starting pointStep 5 Write in the bottomunit of the new fraction (this isthe same as the top unit of yourprevious fraction)Step 6 Write the appropriateconversion factor into thefraction. Your bottom unit willguide you.Step 7 Determine if this topunit is the desired unit (yourfinal destination). In this casethe answer is YES, so we moveon to step 9Step 8 Cancel all diagonal units.Once this is done, your finaldestination should be the onlyunit left in this case secondsStep 9 Multiply the top of thefractions; multiply the bottom ofthe fractions; divide the productof the top by the product of thebottomStarting PointFinal Destination 9. How many centimeters are in 27 inches?27 inches centimeters(27 inches)1( )( )cminch68.58 centimeters2.541=(27)(2.54 cm)(1)(1)=Step 1 Read the question and determinewhat information it provides you with(starting point & final destination) Step 2 Write down yourstarting point and your finaldestination1 inch = 2.54 centimetersStep 3 Determine howyou will getfrom yourstarting pointto your finaldestination (listanyconnectionsor conversionfactors)Step 4 Create a fraction byplacing your starting point overoneStep 5 Write in the bottomunit of the new fraction (this isthe same as the top unit of yourprevious fraction)Step 6 Write the appropriateconversion factor into thefraction. Your bottom unit willguide you.Step 7 Determine if this topunit is the desired unit (yourfinal destination). In this casethe answer is YES, so we moveon to step 9Step 8 Cancel all diagonal units.Once this is done, your finaldestination should be the onlyunit left in this casecentimetersStep 9 Multiply the top of thefractions; multiply the bottom ofthe fractions; divide the productof the top by the product of thebottomStarting PointFinal Destination 10. If a truck weighs 15,356 pounds, how many tonsis it?15,356 pounds tons(15,356 lbs.)1( )( )tonlbs.7.678 tons12000=(15,356)(1 ton)(1)(2000)=Step 1 Read the question and determinewhat information it provides you with(starting point & final destination) Step 2 Write down yourstarting point and your finaldestination2000 pounds = 1 tonStep 3 Determine howyou will getfrom yourstarting point toyour finaldestination (listanyconnections orconversionfactors)Step 4 Create a fraction byplacing your starting point overoneStep 5 Write in the bottomunit of the new fraction (this isthe same as the top unit of yourprevious fraction)Step 6 Write the appropriateconversion factor into thefraction. Your bottom unit willguide you.Step 7 Determine if this topunit is the desired unit (yourfinal destination). In this casethe answer is YES, so we moveon to step 9Step 8 Cancel all diagonal units.Once this is done, your finaldestination should be the onlyunit left in this case tonsStep 9 Multiply the top of thefractions; multiply the bottom ofthe fractions; divide the productof the top by the product of thebottomStarting PointFinal Destination 11. If you had 10.5 gallons of milk, how many pintswould you have?10.5 gallons pints(10.5 gallons)1( )( )quartsgallon84 pints41=(10.5)(4)(2 pints)(1)(1)(1) =Step 1 Read the question and determinewhat information it provides you with(starting point & final destination) Step 2 Write down yourstarting point and your finaldestination1 gallon = 4 quarts1 quart = 2 pintsStep 3 Determine howyou will getfrom yourstarting point toyour finaldestination (listanyconnections orconversionfactors)Step 4 Create a fraction byplacing your starting point overoneStep 5 Write in the bottomunit of the new fraction (this isthe same as the top unit of yourprevious fraction)Step 6 Write the appropriateconversion factor into thefraction. Your bottom unit willguide you.Step 7 Determine if this topunit is the desired unit (yourfinal destination). In this casethe answer is NO, so we moveback to step 5Step 9 Cancel all diagonal units.Once this is done, your finaldestination should be the onlyunit left in this case pintsStep 10 Multiply the top ofthe fractions; multiply thebottom of the fractions; dividethe product of the top by theproduct of the bottomStarting PointFinal Destination( )( )pintsquart21Step 6 Write in the bottomunit of the new fraction (this isStep 8 Write the appropriateconversion factor into thefraction. Your bottom unit willguide you.Step 7 Determine if this topunit is the desired unit (yourfinal destination). In this casethe answer is YES, so we moveon to step 9 12. Students go to school for 180 days. How many minutesis this equal to?180 days minutes(180 days)1( )( )hoursday259,200 minutes241=(180)(24)(60 minutes)(1)(1)(1) =Step 1 Read the question and determinewhat information it provides you with(starting point & final destination) Step 2 Write down yourstarting point and your finaldestination1 day = 24 hours1 hour = 60 minutesStep 3 Determine howyou will getfrom yourstarting point toyour finaldestination (listanyconnections orconversionfactors)Step 4 Create a fraction byplacing your starting point overoneStep 6 Write in the bottomunit of the new fraction (this isthe same as the top unit of yourprevious fraction)Step 7 Write the appropriateconversion factor into thefraction. Your bottom unit willguide you.Step 8 Determine if this topunit is the desired unit (yourfinal destination). In this casethe answer is NO, so we moveback to step 5Step 9 Cancel all diagonal units.Once this is done, your finaldestination should be the only unitleft in this case minutesStep 9 Multiply the top ofthe fractions; multiply thebottom of the fractions;divide the product of the topby the product of thebottomStarting PointFinal Destination( )( )minuteshour601Step 6 Write in the bottomunit of the new fraction (this isthe same as the top unit of yourprevious fraction)Step 8 Write the appropriateconversion factor into thefraction. Your bottom unit willguide you.Step 7 Determine if this topunit is the desired unit (yourfinal destination). In this casethe answer is YES, so we moveon to step 9