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DIMENSIONAL ANALYSIS How to Change Units using Math SI BASE UNITS QUANTITY Length Volume Mass Time Temperature Amount Memory NAME Meter Liter Kilogram gram second Kelvin Celsius mole byte SYMBOL m l Kg g s K C mol b SI System Prefixes piconanomicromillicentiKiloMegaGigaTetra- p n µ m c K M G T 10-12 10-9 10-6 10-3 10-2 103 106 109 1012 Know these prefixes 1/1,000,000,000,000 1/1,000,000,000 1/1,000,000 1/1000 1/100 1000 1,000,000 1,000,000,000 1,000,000,000,000 PUTTING THEM TOGETHER • 1000 meters • 1,000,000 bytes • 1/1000 Liter • 1/100 meter • 1,000,000,000 seconds 1 1 1 1 1 Kilometer Megabyte milliliter centimeter Gigasecond Conversion Fractions • A Conversion Fraction is a Fraction that has the units in it and is equal to one • 1000m/1Km • 100cm/1m • 1000mm/1m • 1000g/1Kg • NOTE: The larger number always goes with the smaller unit Lets try something How many millimeters are in 5 meters 5 m x 1000mm/1m = 5000mm Let’s look at this: We write our starting point first, and then determine the fraction, there are 1000 milli’s in one whole, so the fraction is 1000 mm/1 m Let’s try another How many Kilometers are there in 5000 millimeters? First, remove the starting prefix 5000mm x 1m/1000mm = 5 m Second, place the new prefix 5 m x 1Km/1000m = 0.005 Km Let’s Try Another How many milligrams are in 5000 Kilograms? First, remove the starting prefix: 5000 Kg x 1000g/1Kg = 5000 g Second, place the ending prefix: 5000g x 1000 mg/1g = 5,000,000 mg LET’S LOOK AGAIN How many meters will a car traveling 100 Km/hr travel in 1 minute? – This one is a little harder: You have to make two sets of conversions First Convert 100 Km/hr to meters per hour – Second you have to convert m/hr to m/min – 100 Km/hr x 1000m/1 Km = 1000000 m/hr 1000000 m/hr x 1hr/60 min = 16667 m/min Notice: hr goes on top in the conversion because it is on the bottom in the initial number Some Practice Problems I drive 5 miles to school each morning. How many inches is that? Express your answer in scientific notation. Another one We have seven class periods here at AHS. If you zone out 5 minutes every class period, how many hours of education will you have missed in the 180-day school year? Again If a car is traveling 60 miles per hour, how many inches per second is it moving? And Yet Again Mr Simms wants to give all of his chemistry students enough chocolate to make them goofy for the rest of the day. It's a known fact that it takes 47 chocolate chips to make a student goofy. The average cookie contains 29 chocolate chips. Mr Simms has 5 classes and each class has an average of 32 students. How many toll house cookies does Mr Simms need to make? One Last One If you never learn dimensional analysis, you will have to work at a fast food restaurant for the rest of your life wrapping hamburgers. Each hour you wrap 184 hamburgers. You work 8 hours per day and work 5 days a week. You get paid every 2 weeks with a salary of $840.34. How many hamburgers will you have to wrap to make your first one million dollars?