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Elementary topics ii nov 22nd
- 1. Unit Conversions &Metric Units
- 2. Units conversions swap between different units, such as feet to inches. Example: How many inches are in 3 feet? We know that there are 12 inches in a foot … or 1 foot = 12 inches So, 3x12 = 36 inches
- 3. The metric system is an international decimalized system of measurement. However, in the U.S., we used what is called the standard units.
- 4. Measurement Standard Unit Metric Unit Length/Width Yards, feet, inches Meter, centimeter, millimeter Mass Pounds Gram, milligram, kilogram, metric ton Temperature Fahrenheit Celsius Area Square feet, square Square meters, square yards centimeters Volume Cubic feet Liter, cubic centimeter Speed Miles per hour Meter per second Kilometer per hour
- 6. The metric system was first proposed in France by Gabriel Mouton in 1670. However, it was not until the French Revolution in 1790 where the French Academy of Sciences decided on a common system (at the time, there were 13 distinct measures for a foot)! A meter is a base unit for 1/10,000,000 of the distance from the equator to the North Pole on a meridian through Paris.
- 7. How many centimeters are in 4 inches? 3 cubic feet is how many cubic inches? 5 yards is how many feet? Which is bigger: a kilometer or millimeter? 3 liters is how many quarts? 1,000 cubic centimeters is equivalent to how many liters?
- 8. Length Conversions 1foot = 12 inches 3 feet = 1 yard Example: How many yards are in 60 inches?
- 9. Recall the problemwe just did…how many yards are in 60 inches? Now that we have Notice that the inches Notice that feet units that are in are DIAGONAL from are DIAGONAL from yards (what we This is your wanted), you initial amount each other each other This is key to simply multiple converting. straight across Overall, we want to Our units must cancel. the fractions and convert from inches reduce. And…you’re to yards. The first Now in order to go Now in order to go done! step is to convert from inches to feet, from feet to yards, from inches to feet. you have to put an you have to put an EQUAL conversion EQUAL conversion about it. So about it. So 12 inches = 1 foot 3 feet = 1 yard
- 10. 1 inch = 2.54 centimeters 1 meter = 39.4 inches 1 foot = 30.48 centimeters 1 kilometer = .621 miles Example: How many centimeters are in 10 inches?
- 11. 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 month = 28-31 days (watch for leap years!) 1 year = 12 months Example: How many seconds are there in 5 days?
- 12. 1 dozen = 12 units 12 dozen = 1 gross Example: Suppose we have 36 eggs. How many gross is this?
- 13. 3 teaspoons (tsp) = 1 tablespoon (tbsp) 2 tablespoons = 1 ounce (oz) 8 oz = 1 cup 2 cups = 1 pint (pt) 2 pints = 1 quart 4 quarts = 1 gallon 31.5 gallons = 1 barrel Example: Suppose you have 5 quarts of iced tea. How many cups can you serve?
- 14. Example: 10 oz equals how many teaspoons? Example: 400 pints equals how many gallons?
- 15. Fahrenheit and Celsius Example: If it is 80°F, what is the temperature in Celsius? If it is 32°C, what is the temperature in Fahrenheit?
- 16. 1 Kg = 2.2 lbs 1 liter = 1000 cm3 1 liter = 1.06 qt 1 gal = 3.8 liters 1 ton = 2,000 lbs (short) or 2,240 lbs (long) Example: How many cubic centimeters (cm3) are in 2 liters?
- 17. deci: 1/10 = 10-1 deca: 10 = 101 centi: 1/100 = 10-2 hecto: 100 = 102 milli: 1/1,000 = 10-3 kilo: 1,000 = 103 micro: 1/1000000 = 10-6 mega: 1,000,000 = 106 nano: 10-9 giga: 109 Example: 100 millimeters (mm) is how many centimeters (cm)?
- 18. Base Example: What is bigger: 100 millimeters or 1 kilometer? 1 kilometer!
- 19. When we are dealing with units that are squared (such as when finding area) or cubed (such as when finding volume), we have to be careful with our units! Let’s take a look. Example: A cube’s volume is 1,000 cubic centimeters (cm3). What is its volume in inches? or
- 20. So, I’ve attached a conversion sheet with all of these conversions listed on for you to reference. But, take a look at a few problems and see how you do. I’ll post an answer key either later in the week, or we can go over any questions during our next class.
Editor's Notes
- #6 Pretty much everywhere!
- #10 You probably want to view this as a PowerPoint…. :)Basically when converting, you wish to cancel out your units as you move from one unit to the next.Some require you to use several steps, going from inches -> feet -> yards. Converting requires you to think logically about going from one unit to another, using the proper conversions.
- #12 Your goal is to go from days into seconds.You can do so by: days -> hours -> minutes -> seconds. You know you’re done when your top unit is what the question asks.
- #16 First consider what we want our final units to be in, Celsius or Fahrenheit. Then, look at our given information. Finally, plug our given temperature into our equation to convert it, and simplify.
- #18 Notice for the prefixes, I also included the number represented as an exponent with base 10. This is called scientific notation. Imagine if you were a scientist measuring something incredibly small or big. Scientific notation is just like a “short-hand” way to list these numbers.
- #19 You only need to know the middle most ones, but this gives you an idea to their size, showing each on a number line.
- #20 Think of this like cross-cancelling like you would in algebra. You need to make sure that your units are compatible by cancelling out the centimeters (all three of them) and equating to inches (three making it cubic inches).