Dimensional Analysis A problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html

Dimensional Analysis Unit factors may be made from any two terms that describe the same or equivalent "amounts" of what we are interested in. http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html

Dimensional Analysis We know that 2.54 cm = 1.00 inch We can make two unit factors from this information 1 inch 2.54 cm 2.54 cm 1 inch We can use these unit factors to solve problems http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html

Dimensional Analysis How many centimeters are in 6.00 inches? Express 24 cm in inches http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html

Dimensional Analysis The goal is to arrange the unit factors so that all units cancel except the desired one How many seconds are there in 2 years? Note that 60 min/1 hr = 1 hr/60 min, but only the former is useful in this example http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html

Dimensional Analysis – Tips for Use Don't panic. Figure out what answer unit(s) you want to end up with. This is usually easy. Write down, in math terms, everything you know that relates to the problem. You may need to read the problem several times, rephrasing parts of it, so you can translate everything into math terms. You may need to look up a few conversion factors, but that's inconvenient, not difficult. http://www.alysion.org/dimensional/fun.htm

Dimensional Analysis – Tips for Use Pick a starting factor. If possible pick one that already has one of the units you want in the right place. Otherwise start with something you are given that is not a conversion factor. Plug in conversion factors that allow you to cancel out any units you don't want until you are left with only the units you do want (your answer units). If you can't solve the problem, pick a different starting factor and start over. http://www.alysion.org/dimensional/fun.htm

Dimensional Analysis Do the math. You may be less apt to make an error if you first multiply all the top numbers, then divide by all the bottom numbers. Now double-check your calculations. If you make a mistake it will probably be in hitting the wrong key on the calculator. Ask yourself if the answer seems right or reasonable. If not, recheck everything. http://www.alysion.org/dimensional/fun.htm

Classwork Use dimensional analysis for each problem and solve it Copy the questions into your notebook (right-side) and answer them Use dimensional analysis for each problem and solve it 1) Each pizza at your party has 12 slices Each person eats 4 slices 15 people are coming to your party How many pizzas will be needed? 2) If you are traveling 50 mi/hr, how many feet/second are you travelling? (5280 ft=1mi) 3) You visit the store and find a banana sale. On average 8 bananas weigh one pound. The sale price for bananas is four pounds for $5.00. You decide to treat your advising group to 25 banana splits, 1 banana per split. How much will it cost you to buy 25 bananas? http://www.alysion.org/dimensional/fun.htm 9

Classwork Copy the questions into your notebook (right-side) and answer them 4) You have come down with a bad case of the geebies, but fortunately your grandmother knows how to cure the geebies. She sends you an eyedropper bottle labeled: Take 1 drop per 10 lbs. of body weight per day divided into 4 doses until the geebies are gone. What do you want to know? In order to take one dose 4 times a day you need to know how many drops to take per dose. Translated into math terms you want the answer to be in: drops / dose Assume that you weigh 160 pounds. You know that you need to take 4 doses per day (implied). You know that you need to take 1 drop per 10-lbs. body weight per day. http://www.alysion.org/dimensional/fun.htm 10

Classwork Copy the questions into your notebook (right-side) and answer them 5) The distance to the sun is 1.496 x 1011 meters. The speed of light is 3.00 x 108 m/s. A minute is defined to be 60 seconds. How many seconds does it take light to reach the Earth from the Sun? 6) The formula for gravitational force is F = G m1m2 r2 m1 and m2 in kg and r in m What units does G have to have so that the force is in kg m/s2? http://courses.ma.org/sciences/Hicks/Chemistry/Chemistry%20Worksheets/2-22DimAnalwksht.htm 11

Classwork Use dimensional analysis for each problem and solve it Copy the questions into your notebook (right-side) and answer them Use dimensional analysis for each problem and solve it 1) Each pizza at your party has 12 slices Each person eats 4 slices 15 people are coming to your party How many pizzas will be needed? 2) If you are traveling 50 mi/hr, how many feet/second are you travelling? (5280 ft=1mi) 3) You visit the store and find a banana sale. On average 8 bananas weigh one pound. The sale price for bananas is four pounds for $5.00. You decide to treat your advising group to 25 banana splits, 1 banana per split. How much will it cost you to buy 25 bananas? http://www.alysion.org/dimensional/fun.htm 12

Classwork Copy the questions into your notebook (right-side) and answer them 4) You have come down with a bad case of the geebies, but fortunately your grandmother knows how to cure the geebies. She sends you an eyedropper bottle labeled: Take 1 drop per 10 lbs. of body weight per day divided into 4 doses until the geebies are gone. What do you want to know? In order to take one dose 4 times a day you need to know how many drops to take per dose. Translated into math terms you want the answer to be in: drops / dose Assume that you weigh 160 pounds. You know that you need to take 4 doses per day (implied). You know that you need to take 1 drop per 10-lbs. body weight per day. http://www.alysion.org/dimensional/fun.htm 13

Classwork Copy the questions into your notebook (right-side) and answer them 5) The distance to the sun is 1.496 x 1011 meters. The speed of light is 3.00 x 108 m/s. A minute is defined to be 60 seconds. How many seconds does it take light to reach the Earth from the Sun? 6) The formula for gravitational force is F = G m1m2 r2 m1 and m2 in kg and r in m What units does G have to have so that the force is in kg m/s2? http://courses.ma.org/sciences/Hicks/Chemistry/Chemistry%20Worksheets/2-22DimAnalwksht.htm 14