2Dimensional Analysis Example: 1 in. = 2.54 cm Conversion Factors : Fractions in which the numerator and denominator are EQUAL quantities, expressed in different unitsExample: in. = 2.54 cmFactors: 1 in and cm2.54 cm in.
3Conversion Factors 1. Dollars and cents 2. Liters and mL Write conversion factors that relate each of the following pairs of units:1. Dollars and cents2. Liters and mL3. Hours and minutes4. Meters and kilometers
4How many minutes are in 2.5 hours? Sample ProblemHow many minutes are in 2.5 hours?Conversion factors: 1hr or 60min60min hrcancel2.5 hr x60min1hr= minBy using dimensional analysis, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!
5Steps to Problem Solving Write down the given amount. Don’t forget the units!Multiply by a conversion faction.Use the fraction as a conversion factorThe denomninator is the givenThe numerator is what you are lookingIf you can’t convert directly, use one that you know and keep convertingMultiply and divide the units (Cancel)Multiply and divide the numbers.Write the answer
6Let’s try it!What units do we use to measure time? (list from smallest to biggest)How many seconds in a year?
7Check PointUse the steps to solving a problem to answer the next questions:How rattlesnake is 2.44 m long. How long is the snake in cm?How many seconds are in 1.4 years?You have $7.25 in your pocket in quarters. How many quarters do you have?If Jacob stands on Spencer’s shoulders, they are two and a half yards high. How many inches is that? (1 yard = 3 ft., 12in = 1ft.)
9Check Point #2 Solve using dimensional analysis: You have $7.25 in your pocket in quarters. How many quarters do you have?If Jacob stands on Spencer’s shoulders, they are two and a half yards high. How many inches is that? (1 yard = 3 ft., 12in = 1ft.)
10Jaberwacky problem There are 20 tumtum trees in the tulgey wood. In each tulgey wood is one frumious Bandersnatch.There are 5 slithy toves in 2 borogoves.There are 2 mome raths per Jabberwock.There are 2 Jubjub birds in 200 tumtum trees.There are 200 mome raths in each borogove.There are 5 Jubjub birds per slithy tove.The question is: If there are 5 frumious Bandersnatches, how many Jabberwocks are there?You should use a dimensional analysis setup to show your work!HINT: What information above is a conversion factor and what information is not?