2. METRIC CONVERSION Count Up to Six and Know Your Left From Your Right

3. What are Metric Conversions? Sometimes we need to change from one measurement to another. This is usually done because the unit that is used is either too big or too small for that type of measurement.

4. TOO BIG !!! 525,568 millimeters Sometimes the number is too big for the unit being measured.

5. Too Small.00654 km Sometimes the number is too small for the unit being measured

6. How Do We Fix This Problem? We can correct these problems by doing a process called Metric Conversion. When you do a Metric Conversion, you are changing from one unit of measurement to another.

7. So How Do I Do A Metric Conversion? We will be using a method called The Stair-step Method of Metric Conversion. It requires two things; one, that you be able to count to 6, and two, that you know your left from your right.

8. The Stair-step Kilo- Hecto- Deka- base units Deci- Centi- Milli- Grams, liters,meters

9. How Do I Use This? The first letter of the prefix in the unit of measurement tells you which step to start on. The first letter in the second unit of measurement tells you which step to stop on. Find which step to start on, and count the number of steps it takes to get to the step that you need to stop on. If you went to the right(downstairs) the decimal in the first measurement moves that many places to the right. If you went to the left (upstairs) then the decimal moves to the left. Fill any empty places with zeros.

10. How Do I Use This (cont.)? If there is only one letter in the unit of measurement, then you start or stop on the base unit step. Now let’s look at our examples…..

11. 525568 mm = ? m Millimeters are a very small amount of distance. You would not want to measure a large distance in a very small unit. To make the conversion, we start on the milli- step and go three steps to the left to get to the meter step. Therefore, the decimal in 525568 mm moves three places to the left, becoming 525.568 m.

12. .00654 km = ? m Kilometers are a fairly large unit of distance. You would not want to measure a small distance in a large unit, so we need to convert it to a smaller unit, the meter. We would start on the Kilo- step and move three steps to the right this time, ending on the meter (base unit) step. Therefore,.00654 km becomes 6.54 m.

13. Hey! This Is Easy! You bet it’s easy! Like we said on the first slide….. Be able to count up to six and know your left from your right. Now, get your stair-step sheet and your practice problems and do some more conversions!

14. Steps to Problem Solving 1.Write down the given amount. Don’t forget the units! 2.Multiply by a fraction. 3.Use the fraction as a conversion factor. Determine if the top or the bottom should be the same unit as the given so that it will cancel. 4.Put a unit on the opposite side that will be the new unit. If you don’t know a conversion between those units directly, use one that you do know that is a step toward the one you want at the end. 5.Insert the numbers on the conversion so that the top and the bottom amounts are EQUAL, but in different units. 6.Multiply and divide the units (Cancel). 7.If the units are not the ones you want for your answer, make more conversions until you reach that point. 8.Multiply and divide the numbers. Don’t forget “Please Excuse My Dear Aunt Sally”! (order of operations)

15. SI measurement Le Système international d'unitésLe Système international d'unités The only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularlyThe only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly Metrication is a process that does not happen all at once, but is rather a process that happens over time.Metrication is a process that does not happen all at once, but is rather a process that happens over time. Among countries with non- metric usage, the U.S. is the only country significantly holding out.The U.S. officially adopted SI in 1866.Among countries with non- metric usage, the U.S. is the only country significantly holding out. The U.S. officially adopted SI in 1866. Information from U.S. Metric Association

16. Chemistry In Action On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat. 1 lb = 1 N 1 lb = 4.45 N “This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

17. Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard. For example, at one time the standard for length was the king’s foot. What are some problems with this standard?

18. Accuracy vs. Reproducibility/Precision Accuracy- How close a measurement is to its true or actual value. Reproducibility/Precision- How close a group of measurements are to each other

19. Stating a Measurement In every measurement there is a  Number followed by a  Unit from a measuring device The number should also be as precise as the measurement!

20. UNITS OF MEASUREMENT Use SI units — based on the metric system LengthMassVolumeTimeTemperature Meter, m Kilogram, kg Seconds, s Celsius degrees, ˚C kelvins, K Liter, L

21. Mass vs. Weight Mass: Amount of Matter (grams, measured with a BALANCE)Mass: Amount of Matter (grams, measured with a BALANCE) Weight: Force exerted by the mass, only present with gravity (pounds, measured with a SCALE)Weight: Force exerted by the mass, only present with gravity (pounds, measured with a SCALE) Can you hear me now?

22. Some Tools for Measurement Which tool(s) would you use to measure: A. temperature B. volume C. time D. weight

23. Learning Check Match L) length M) mass V) volume ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g Aspirin. ____ D. A bottle contains 1.5 L of water. M L M V

24. Learning Check What are some U.S. units that are used to measure each of the following? A. length B. volume C. weight D. temperature

25. Metric Prefixes Kilo- means 1000 of that unitKilo- means 1000 of that unit –1 kilometer (km) = 1000 meters (m) Centi- means 1/100 of that unitCenti- means 1/100 of that unit –1 meter (m) = 100 centimeters (cm) –1 dollar = 100 cents Milli- means 1/1000 of that unitMilli- means 1/1000 of that unit –1 Liter (L) = 1000 milliliters (mL)

26. Metric Prefixes

28. Learning Check 1. 1000 m = 1 ___a) mm b) km c) dm 2. 0.001 g = 1 ___ a) mg b) kg c) dg 3. 0.1 L = 1 ___a) mL b) cL c) dL 4. 0.01 m = 1 ___ a) mm b) cm c) dm

29. Units of Length ? kilometer (km) = 500 meters (m)? kilometer (km) = 500 meters (m) 2.5 meter (m) = ? centimeters (cm)2.5 meter (m) = ? centimeters (cm) 1 centimeter (cm) = ? millimeter (mm)1 centimeter (cm) = ? millimeter (mm) 1 nanometer (nm) = 1.0 x 10 -9 meter1 nanometer (nm) = 1.0 x 10 -9 meter O—H distance = 9.4 x 10 -11 m 9.4 x 10 -9 cm 0.094 nm O—H distance = 9.4 x 10 -11 m 9.4 x 10 -9 cm 0.094 nm

30. Learning Check Select the unit you would use to measure 1. Your height a) millimeters b) meters c) kilometers 2. Your mass a) milligramsb) grams c) kilograms 3. The distance between two cities a) millimetersb) meters c) kilometers 4. The width of an artery a) millimetersb) meters c) kilometers

31. Dimensional Analysis

32. What is Dimensional Analysis? Have you ever used a map? Since the map is a small-scale representation of a large area, there is a scale that you can use to convert from small-scale units to large- scale units—for example, going from inches to miles or from cm to km.

33. What is Dimensional Analysis? Ex: 3 cm = 50 km

34. What is Dimensional Analysis? Have you ever been to a foreign country? One of the most important things to do when visiting another country is to exchange currency. For example, one United States dollar equals 1535.10 Lebanese Pounds.

35. What is Dimensional Analysis? Whenever you use a map or exchange currency, you are utilizing the scientific method of dimensional analysis.

36. What is Dimensional Analysis? Dimensional analysis is a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value. It is used to go from one unit to another.

37. How Does Dimensional Analysis Work? A conversion factor, or a fraction that is equal to one, is used, along with what you’re given, to determine what the new unit will be.

38. How Does Dimensional Analysis Work? In our previous discussions, you could say that 3 cm equals 50 km on the map or that $1 equals 1535.10 Lebanese Pounds (LBP).

39. How Does Dimensional Analysis Work? If we write these expressions mathematically, they would look like 3 cm = 50 km $1 = 1535.10 LBP

40. Examples of Conversions 60 s = 1 min 60 min = 1 h 24 h = 1 day

41. Examples of Conversions You can write any conversion as a fraction. Be careful how you write that fraction. For example, you can write 60 s = 1 min as 60s or 1 min 1 min 60 s

42. Examples of Conversions Again, just be careful how you write the fraction. The fraction must be written so that like units cancel.

43. Steps 1.Start with the given value. 2.Write the multiplication symbol. 3.Choose the appropriate conversion factor. 4.The problem is solved by multiplying the given data & their units by the appropriate unit factors so that the desired units remain. 5.Remember, cancel like units.

44. Let’s try some examples together… 1.Suppose there are 12 slices of pizza in one pizza. How many slices are in 7 pizzas? Given: 7 pizzas Want: # of slices Conversion: 12 slices = one pizza

45. 7 pizzas 1 Solution Check your work… X 12 slices 1 pizza = 84 slices

46. Let’s try some examples together… 2. How old are you in days? Given: 17 years Want: # of days Conversion: 365 days = one year

47. Solution Check your work… 17 years 1 X 365 days 1 year = 6052 days

48. Let’s try some examples together… 3. There are 2.54 cm in one inch. How many inches are in 17.3 cm? Given: 17.3 cm Want: # of inches Conversion: 2.54 cm = one inch

49. Solution Check your work… 17.3 cm 1 X 1 inch 2.54 cm = 6.81 inches Be careful!!! The fraction bar means divide.

50. Now, you try… 1.Determine the number of eggs in 23 dozen eggs. 2.If one package of gum has 10 pieces, how many pieces are in 0.023 packages of gum?

51. Multiple-Step Problems Most problems are not simple one-step solutions. Sometimes, you will have to perform multiple conversions. Example: How old are you in hours? Given: 17 years Want: # of days Conversion #1: 365 days = one year Conversion #2: 24 hours = one day

52. Solution Check your work… 17 years 1 X 365 days 1 year X 24 hours 1 day = 148,920 hours

53. Combination Units Dimensional Analysis can also be used for combination units. Like converting km/h into cm/s. Write the fraction in a “clean” manner: km/h becomes km h

54. Combination Units Example: Convert 0.083 km/h into m/s. Given: 0.083 km/h Want: # m/s Conversion #1: 1000 m = 1 km Conversion #2: 1 hour = 60 minutes Conversion #3: 1 minute = 60 seconds

55. 83 m 1 hour Solution Check your work… 0.083 km 1 hour X 1000 m 1 km X 1 hour 60 min = 0.023 m sec 83 m 1 hour X 1 min 60 sec =