Metric and dimensional analysis
- 1. Kilo Hecto Deka UNITS Gram Liter Meter UNITS deci centi milli Metric to Metric Map “Use it and you will never get lost!” How To Use Your Map 1) Start at the unit/prefix given to you (starting point). 2) Count the number of steps/places to the unit/prefix you want (final destination)each is a factor of 10. 3) Move the decimal point the number of steps/places in the same direction. SMALLESTLARGEST
- 2. Kilo Hecto Deka Gram deci centi milli Check for Understanding How many mg are in 3.6 Kg? Starting point Final Destination 3,600,000 mg6 places to the right of the decimal point
- 3. Kilo Hecto Deka Meter deci centi milli Check for Understanding How many hm are in 12.67 mm? Starting pointFinal Destination 0.0001267 hm5 places to the left of the decimal point
- 4. Helpful Mnemonic Try to create your own mnemonic to help you remember the prefixes and their order. This will be important because you will not receive the metric map on your quiz. Kings Have Diamonds BUT Diamonds Cost Money
- 5. 1. Read the question. The question will provide you with information that identifies your starting point and your final destination. • Starting point = the number and unit provided by the question • Final destination = the units desired after converting 2. Write your starting point and your final destination. 3. Determine how you will get from your starting point to your final destination (simply find “connections” or conversion factors between your 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 the top unit of the previous fraction. 6. Write one set of “connections” or conversion factors into the fraction. Your bottom unit will guide you. 7. Ask yourself, “Do I have the desired unit (final destination) on the top of the new fraction?” NO YES 8. Cancel any units that are diagonal. (This should leave you with only the units that represent your final destination) 9. Multiply the top of the fractions…multiply the bottom of the fractions…divide the top by the bottom. (Go back to step 5) (Proceed to step 8)
- 7. Practice Conversions 1. How many seconds are in 6 minutes? 360 seconds 2. How many centimeters are in 27 inches? 68.58 centimeters 3. If a truck weighs 15,356 pounds, how many tons is it? 7.678 tons 4. If you had 10.5 gallons of milk, how many pints would you have? 84 pints 5. Students go to school for 180 days. How many minutes is this equal to? 259,200 minutes
- 8. How many seconds are in 6 minutes? 6 minutes seconds (6 minutes) 1 ( ) ( ) seconds minute 360 seconds 60 1 = (6)(60 seconds) (1)(1) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination1 minute = 60 seconds Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction with your starting point Step 5 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 6 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 7 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 8 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case seconds Step 9 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting PointFinal Destination
- 9. How many centimeters are in 27 inches? 27 inches centimeters (27 inches) 1 ( ) ( ) cm inch 68.58 centimeters 2.54 1 = (27)(2.54 cm) (1)(1) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination1 inch = 2.54 centimetersStep 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction by placing your starting point over one Step 5 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 6 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 7 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 8 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case centimeters Step 9 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting PointFinal Destination
- 10. If a truck weighs 15,356 pounds, how many tons is it? 15,356 pounds tons (15,356 lbs.) 1 ( ) ( ) ton lbs. 7.678 tons 1 2000 = (15,356)(1 ton) (1)(2000) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination2000 pounds = 1 tonStep 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction by placing your starting point over one Step 5 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 6 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 7 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 8 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case tons Step 9 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting PointFinal Destination
- 11. If you had 10.5 gallons of milk, how many pints would you have? 10.5 gallons pints (10.5 gallons) 1 ( ) ( ) quarts gallon 84 pints 4 1 = (10.5)(4)(2 pints) (1)(1)(1) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 gallon = 4 quarts 1 quart = 2 pintsStep 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction by placing your starting point over one Step 5 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 6 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 7 – Determine if this top unit is the desired unit (your final destination). In this case the answer is NO, so we move back to step 5 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case pints Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting PointFinal Destination ( ) ( ) pints quart 2 1 Step 6 – Write in the bottom unit of the new fraction (this is Step 8 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 7 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9
- 12. Students go to school for 180 days. How many minutes is this equal to? 180 days minutes (180 days) 1 ( ) ( ) hours day 259,200 minutes 24 1 = (180)(24)(60 minutes) (1)(1)(1) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 day = 24 hours 1 hour = 60 minutesStep 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors)Step 4 – Create a fraction by placing your starting point over one Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is NO, so we move back to step 5 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case minutes Step 9 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting PointFinal Destination ( ) ( ) minutes hour 60 1 Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 8 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 7 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9