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# Measurement&Conversions

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### Measurement&Conversions

1. 1. We need a reliable system of measurement to obtain useful data.
2. 2. Before standardized units: <ul><li>Measurement used to be subjective </li></ul><ul><ul><li>One “foot” really was the length of a human foot. Obviously, foot size varies. </li></ul></ul><ul><li>In order to have consistency, there is a need for a standardized system of units. </li></ul><ul><ul><li>One foot should be the same length for every person. </li></ul></ul>
3. 3. International System (S.I.) of Units: <ul><li>Developed in the late 1700s </li></ul><ul><li>You may recognize as the “Metric” system. </li></ul><ul><li>Our “English” system was eventually standardized also, but the S.I. system is used by most countries and the international scientific community. </li></ul><ul><ul><li>We will use the S.I. system in class. </li></ul></ul><ul><ul><li>Based on 10– What is English system based on? </li></ul></ul>
4. 4. S.I. Base Units: <ul><li>Base units can be measured directly. Units for other measurements are calculated from base units. </li></ul><ul><li>* One meter is equal to approximately 3 feet, 3 inches. </li></ul>s second time K, °C Kelvin, deg. Celsius temperature g gram mass m meter length S.I. Abbrev. S.I. Unit Measurement
5. 5. Prefixes <ul><li>kilo- (k), 1000 times </li></ul><ul><li>centi- (c), 1/100 th (There are 100 cents in one dollar.) </li></ul><ul><li>milli- (m), 1/1000 th </li></ul><ul><li>Example: </li></ul><ul><li>1 km = 1000 meters </li></ul><ul><li>1 cm = 0.01 meter (100 cm = 1 m) </li></ul><ul><li>1 mm = 0.001 meter (1000 mm = 1 m) </li></ul>
6. 6. What does this mean? <ul><li>1 kilometer (km) is approximately 0.6 miles </li></ul><ul><li>1 meter (m) is approximately the length from your fingertips to your opposite shoulder </li></ul><ul><li>1 centimeter (cm) is approximately the width of the tip of your pinky </li></ul><ul><ul><li>2.54 cm = 1 inch </li></ul></ul><ul><li>1 millimeter (mm) is approximately the width of a paperclip wire </li></ul>
7. 7. <ul><li>Is this a ridiculous speed limit sign? </li></ul><ul><li>What does it mean? </li></ul><ul><li>120 km/h = 75 mi/h </li></ul>
8. 8. How do they fit together? <ul><li>10 mm = 1 cm </li></ul><ul><li>100 cm = 1 m </li></ul><ul><li>1000 m = 1 km </li></ul>
9. 9. Converting units: <ul><li>Convert 1 km to centimeters. </li></ul><ul><ul><li>Known: 1 km = 1000 m, 1 m = 100 cm </li></ul></ul><ul><ul><li>Therefore, 1000 m = 1 and 100 cm = 1 </li></ul></ul><ul><ul><li> 1 km 1 m </li></ul></ul><ul><ul><li>1 km x 1000 m x 100 cm = 100,000 cm </li></ul></ul><ul><ul><li> 1 km 1 m </li></ul></ul><ul><ul><li>1 km 1000 m 100 cm = 100,000 cm </li></ul></ul><ul><ul><li> 1 km 1 m </li></ul></ul>
10. 10. <ul><li>Mass is a measure of the amount of matter (stuff) that something is made of. </li></ul>Would you expect an elephant or a mouse to have a greater mass? An elephant is made of a greater amount of stuff and, therefore, has a greater mass. In this class we will measure mass in grams or kilograms . The mass of a penny is about 2 ½ to 3 grams. The mass of your teacher is about 50,000 grams (50 kg). The mass of an elephant is about 5,000,000 grams (5,000 kg).
11. 11. Are mass and weight the same? We will compare mass and weight later. However, we measure mass with the same equipment we use to measure weight– a scale or “beam balance”. VB-302-3000 Electronic Precision Balance Scale [Online]. Flex Weigh Direct 2006-07. http://www.flexweighdirect.com/vb3023000/ The mass of this object is 2000 grams.
12. 12. S.I. Derived Units <ul><li>Derived units are combinations of base units. </li></ul><ul><li>Measurements of size: </li></ul><ul><ul><li>Length is a 1-dimensional </li></ul></ul><ul><ul><li>size measured in </li></ul></ul><ul><ul><li>meters (m)  base unit. </li></ul></ul><ul><ul><li>Area is a 2-dimensional size </li></ul></ul><ul><ul><li>measured in </li></ul></ul><ul><ul><li>square meters (m 2 ). </li></ul></ul><ul><ul><li>Volume is a 3-dimensional </li></ul></ul><ul><ul><li>size measured in </li></ul></ul><ul><ul><li>cubic meters (m 3 ). </li></ul></ul><ul><ul><li>Area and volume are </li></ul></ul><ul><ul><li>given in derived units. </li></ul></ul>3 m 3 m 3 m 3 m 3 m 3 m The length of this line = 3 m. The area of this square = 3 m x 3 m = 9 m 2 . The volume of this cube = 3 m x 3 m x 3m = 27 m 3 .
13. 13. <ul><li>What is the area of a sheet of computer paper? </li></ul><ul><li> Area is a 2-dimensional measurement. </li></ul><ul><li> Area = length x width </li></ul><ul><li> Area = 0.22 m x 0.28 m </li></ul><ul><li> Area = 0.062 m 2 </li></ul><ul><li>Square meters are a </li></ul><ul><li>combination of meters </li></ul><ul><li>(meters x meters)  </li></ul><ul><li>derived unit. </li></ul>0.22 m 0.28 m
14. 14. <ul><li>Volume is a measure of the amount of space something occupies or contains. </li></ul><ul><li>Imagine a pool ball and a tennis ball. </li></ul><ul><li>Compare the mass and volume of the two objects. </li></ul><ul><li>The two objects occupy approximately the same amount of space and so have approximately equal volumes. </li></ul><ul><li>The pool ball has a much greater mass than the tennis ball, as you can tell when you pick up the two objects. </li></ul><ul><li>Compare the mass and volume of a basketball and a bowling ball. </li></ul>
15. 15. We use volume measurements everyday. Example: The gas tank in my car contains 15 gallons of gasoline (when it is full). Example: A bread recipe calls for 2 cups of water and 3 tablespoons of oil. In science class, the unit we will use to measure the volumes of liquids is the liter (L) . Think of the amount of space occupied by a 1-liter or 2-liter bottle of soda.
16. 16. The equipment we will use to measure liquid volume in class will be the beaker and the graduated cylinder . Beakers are generally used to measure larger volumes. They do not have many markings. 250 ml Bomex Glass Beaker [Online]. Research Laboratory Supply, Inc. 2008. Researchsupply.net Graduated Cylinder, Glass, 50 ml [Online]. Science Stuff, Inc. 2008. Sciencestuff.com. Graduated cylinders get their name from many small markings (similar to a ruler) that are used to take a wide variety of large and small measurements.
17. 17. <ul><li>What volume of water does an Olympic-sized swimming pool contain? </li></ul><ul><li> Volume is a 3-dimensional measurement. </li></ul><ul><li> Volume = length x width x height (depth). </li></ul><ul><li> Since area = length x width, </li></ul><ul><li>then volume = area x height. </li></ul>width = 25 m length = 50 m depth = 2 m Volume = l x w x d Volume = 50 m x 25 m x 2 m Volume = 2500 m 3
18. 18. 25 m 2 m 50 m Volume = 2 m x 25 m x 50 m Volume = 2500 m 3 This volume is equivalent to 2500 cubes of 1 m 3 (1 m x 1 m x 1 m)
19. 19. <ul><li>So is volume measured in cubic meters (m 3 ) or in liters (L)? </li></ul><ul><ul><li>Solids measured in m 3 only. </li></ul></ul><ul><ul><li>Liquids and gases measured in m 3 or L. </li></ul></ul><ul><li>What is the connection? </li></ul><ul><ul><li>1 cm 3 = 1 mL for liquids and gases </li></ul></ul><ul><ul><li> This is the conversion factor , which allows us to convert a measurement from one type of units to another. </li></ul></ul>