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DIMENSIONAL ANALYSIS

DIMENSIONAL ANALYSIS. How to Change Units using Math. Examples:. How many centimeters are in 2 miles? How many pounds are in 54 kilograms? How many seconds are in 16 years?. SI BASE UNITS. QUANTITY NAME SYMBOL Length Meter m Volume Liter l Mass gram g Time second s

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DIMENSIONAL ANALYSIS

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  1. DIMENSIONAL ANALYSIS How to Change Units using Math

  2. Examples: • How many centimeters are in 2 miles? • How many pounds are in 54 kilograms? • How many seconds are in 16 years?

  3. SI BASE UNITS QUANTITY NAME SYMBOL Length Meter m Volume Liter l Mass gram g Time second s Memory byte b

  4. SI System Prefixes • micro- µ 10-6 1/1,000,000 • milli- m 10-3 1/1000 • centi- c 10-2 1/100 • Kilo- K 103 1000 • Mega- M 106 1,000,000 • Giga- G 109 1,000,000,000 • Know these prefixes

  5. PUTTING THEM TOGETHER • 1000 meters 1 Kilometer • 1,000,000 bytes 1 Megabyte • 1/1000 Liter 1 milliliter • 1/100 meter 1 centimeter • 1,000,000,000 bytes 1 Gigabyte

  6. Conversion Fractions • A Conversion Fraction is a Fraction that has the units in it and is equal to one. • Examples: 1000m1 gram 1Km 1000 mg NOTE: The larger number always goes with the smaller unit

  7. Let’s try a dimensional analysis problem: • How many feet are in 25 miles ? Important!!! The first two required steps in any DA problem are: 1. Write down the number and unit in the question. 2. Put that unit in the denominator of the first conversion factor.

  8. Let’s try a dimensional analysis problem: • How many feet are in 25 miles ?

  9. Let’s try another: • How many pounds are in 175 ounces?

  10. Let’s try a two step problem: • How many miles are in 25 inches?

  11. Another two step problem: • How many seconds are in 24 hours?

  12. An NFL lineman weighs 320 pounds. How many kilograms is that?(454 g = 1 pound)

  13. If a car is traveling 60 miles per hour, how many inches per second is it moving? Sometimes, you’ll have to change the units in the numerator and the denominator:

  14. If a car is traveling 60 miles per hour, how many meters per day is it moving? Sometimes, you’ll have to change the units in the numerator and the denominator:

  15. What if the units have an exponent? • If a home has an area of 2350 ft2, what is the area in square inches?

  16. The density of water is 1.0 gram/cubic cm. What is the density in pounds/cubic ft? (There are 454 grams in a pound, and 2.54 cm in an inch.)

  17. 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?

  18. You're throwing a pizza party for 15 people, and figure each person might eat 4 slices. You call up the pizza place and learn that each pizza will cost you $14.78 and will be cut into 12 slices. How much money do you need? 

  19. An Atascocita High School Honors student was applying to college and wondered how many applications she needed to send. Her counselor explained that with the excellent grade she received in chemistry she would probably be accepted to one school out of every three to which she applied. [3 applications = 1 acceptance] She immediately realized that for each application she would have to write 3 essays, [1 application = 3 essays] and each essay would require 2 hours work [1 essay = 2 hours]. Of course writing essays is no simple matter. For each hour of serious essay writing, she would need to expend 500 calories [1 hour = 500 calories] How many calories will she expend to get 10 acceptances?

  20. A chemistry teacher working at a golf camp during the summer found a liquid which caused him to hit a hole in one time after time! He thought that this was an important liquid to identify, so he set out to determine its density. He found that a sample of the liquid had a mass equal to 455 golf balls and occupied a volume of 620 of the water cups that he obtained at the 7th hole. Each golf ball had a mass of 50 g and the water cups at the 7th hole of the golf course held 45 mL each. What is the density of the unknown liquid in g/ml?

  21. Mrs. Marts wants to give all of her 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. Mrs. Marts has 5 classes and each class has an average of 32 students. How many toll house cookies does Mrs. Marts need to make?

  22. 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?

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