notes: dimensional analysis. dimensional analysis in chemistry and every-day life you will often...
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Notes: Dimensional Analysis
Dimensional Analysis• In Chemistry and every-day life you will
often need to express a measurement using a different unit than the one that was initially used.
• To convert between units we can use dimensional analysis.
• Dimensional analysis is a way to analyze and solve problems by using the units, or dimensions, of the measurements.
Dimensional Analysis• To convert units, conversion factors are used.• Conversion factors are equalities arranged as a
ratio with different units.• For every equality, you can write two conversion
factors
Ex. 1 dollar = 4 quarters
Read as “one dollar per four quarters” or “four quarters per dollar”
Dimensional Analysis• Correctly setting up dimensional analysis problems
is essential to being able to solve them.
Steps of Dimensional Analysis
1.Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3.Multiply by the correct conversion factor
4.Cancel the units and do the math.
Dimensional AnalysisEx. How many dollars are in 27 quarters?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
Dimensional AnalysisEx . How many dollars are in 27 quarters?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
Dimensional AnalysisEx . How many quarters are in 12.75 dollars?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
Dimensional AnalysisEx . How many quarters are in 12.75 dollars?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
Dimensional AnalysisEx. Your car gets 19.5 miles per gallon. How many
miles can you drive on 12.2 gallons of gas?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
Dimensional AnalysisEx. Your car gets 19.5 miles per gallon. How many
miles can you drive on 12.2 gallons of gas?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
Dimensional AnalysisSometimes we need to use several conversion factors
in a row. Usually a go-between unit is used.
Ex. How many seconds are in 5.6 hours?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
Dimensional AnalysisSometimes we need to use several conversion factors
in a row. Usually a go-between unit is used.
Ex. How many seconds are in 5.6 hours?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
1 minute = 60 seconds 1 hour = 60 minutes
note: 2 sig figs needed in answer!!
Dimensional AnalysisSometimes we need to use several conversion factors
in a row. Usually a go-between unit is used.
Ex. How many hours in 12,894 seconds?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
Dimensional AnalysisSometimes we need to use several conversion factors
in a row. Usually a go-between unit is used.
Ex. How many hours in 12,894 seconds?1. Write down the conversion factors you can use
2. Write what is unknown equal to the known.
3. Multiply by the correct conversion factor
4. Cancel the units and do the math.
1 minute = 60 seconds 1 hour = 60 minutes