Metrics Basics


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  • English units are the historical units of measurement in medieval England which evolved as a combination of the Anglo-Saxon and Roman systems of units. They were redefined in England in 1824 by a Weights and Measures Act, which retained many but not all of the unit names with slightly different values, and again in the 1970s by the International System of Units as a subset of the metric system. In modern UK usage, the term is considered ambiguous, as it could refer either to the imperial system used in the UK, or to the US customary system of unit. The common term used in the UK for the non-metric system is imperial units or imperial measurements , since they were used as a standard throughout the British Empire and the Commonwealth. Within the United States, the same term is commonly used to refer to the United States Customary System[1], which retains some unit names but with different values, as well as to the imperial units.
  • Various standards have applied to English units at different times, in different places, and for different applications. Prior to the Battle of Hastings in 1066 the Anglo-Saxon system of measurement had been based on the units of the barleycorn and the gyrd (rod), inherited from tribes from Germany . After the Norman conquest , Roman units were reintroduced. The resultant system of English units was a combination of the Anglo-Saxon and Roman systems. Barleycorn  Basic Anglo-Saxon unit, the length of a corn of barley . The unit survived after 1066 , as the base unit from which the inch was nominally defined. 3 barleycorns comprising 1 inch was the legal definition of the inch in many medieval laws, both of England and Wales, from the 10th century Laws of Hywel Dda to the 1324 definition of the inch enacted by Edward II . Note the relation to the grain unit of weight . This archaic measure is still the basis for current UK and U.S. shoe sizes , with the largest shoe size taken as thirteen inches (a size 13) and then counting backwards in barleycorn units, [4] although the original derivation was: less than 13 barleycorns: infants with no shoes; 13 to 26 barleycorns: children's sizes 1 to 12; 26 to 39 barleycorns: men's sizes 1 to 13.
  • abbreviated SI from French : Système international d'unités [
  • So if you needed to measure length you would choose meter as your base unit Length of a tree branch 1.5 meters Length of a room 5 meters Length of a ball of twine stretched out 25 meters
  • Metrics Basics

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    4. 4. Metric System Basics
    5. 5. English Metric
    6. 6. English units Metric units 12 inches to a foot 3 feet to a yard 1760 yards in a mile 2 cups in a pint 4 quarts in a gallon 16 ounces in a pound 2000 pounds in a ton 100 cm = 1 meter 1000 m = 1 kilometer 100 cL = 1 Liter 1000 L = 1 kiloliter 100 cg = 1 gram 1000 g = 1 kilogram
    7. 7. Metric System Units <ul><li>Base units for different measurements </li></ul><ul><ul><ul><li>Length = meter </li></ul></ul></ul><ul><ul><ul><li>Volume = liter </li></ul></ul></ul><ul><ul><ul><li>Weight (Mass) = gram </li></ul></ul></ul><ul><ul><ul><li>Temperature = degrees Celsius </li></ul></ul></ul>
    8. 8. Metric System <ul><li>Prefix changes the scale of base units </li></ul><ul><ul><li>Example: </li></ul></ul><ul><ul><ul><li>Centi + meter = Centimeter = 100 meters </li></ul></ul></ul><ul><ul><ul><li>Kilo + liter = Kiloliter = 1000 liters </li></ul></ul></ul>
    9. 9. Metric System <ul><li>Scale is based on powers of ten: </li></ul><ul><ul><li>kilo (1000) </li></ul></ul><ul><ul><li>centi (1/100) </li></ul></ul><ul><ul><li>milli (1/1000) </li></ul></ul>milli centi deci Base Units meter gram liter deca hecto kilo 0.001 0.01 0.1 1 10 100 1000
    10. 10. <ul><li>meter is the base unit for length </li></ul><ul><ul><li>Length of a tree branch </li></ul></ul><ul><ul><ul><li>1.5 meters </li></ul></ul></ul><ul><ul><li>Length of a room </li></ul></ul><ul><ul><ul><li>5 meters </li></ul></ul></ul><ul><ul><li>Length of a ball of twine stretched out </li></ul></ul><ul><ul><ul><li>25 meters </li></ul></ul></ul>
    11. 11. <ul><li>What about a longer distance, like from your house to school? </li></ul><ul><ul><li>Let’s say you live 10 miles from school </li></ul></ul><ul><ul><ul><li>10 miles = 16093 meters </li></ul></ul></ul><ul><ul><li>16093 is a big number </li></ul></ul><ul><ul><li>what if you could add a prefix onto the base unit to make it easier to manage? </li></ul></ul><ul><ul><ul><li>16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place) </li></ul></ul></ul>
    12. 12. <ul><li>These prefixes are based on powers of 10. </li></ul><ul><ul><li>From each prefix every “step” is either: </li></ul></ul><ul><ul><ul><li>10 times larger </li></ul></ul></ul><ul><ul><ul><ul><li>or </li></ul></ul></ul></ul><ul><ul><ul><li>10 times smaller </li></ul></ul></ul><ul><ul><li>For example: </li></ul></ul><ul><ul><ul><li>Centimeters are 10 times larger than millimeters </li></ul></ul></ul><ul><ul><ul><li>1 centimeter = 10 millimeters </li></ul></ul></ul><ul><ul><li>Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length </li></ul></ul>milli centi deci Base Units meter gram liter deca hecto kilo 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 40 41 41 40 1 cm
    13. 13. Converting Units (multiply method) <ul><li>For each “step” to the right, you multiply by 10 </li></ul><ul><li>Example: a base unit (liter or gram) to centi </li></ul><ul><ul><li>1 liter = 10 deciliters = 100 centiliters </li></ul></ul><ul><ul><li>2 grams = 20 decigrams = 200 centigrams </li></ul></ul>( 1 x 10 = 10) = (10 x 10 = 100) (2 x 10 = 20) = (20 x 10 = 200) milli centi deci meter liter gram deca hecto kilo
    14. 14. <ul><li>For each “step” to the right, you move the decimal in the same direction </li></ul><ul><ul><li>Example: change meters to centimeters </li></ul></ul><ul><ul><li>1 meter = 10 decimeters = 100 centimeters </li></ul></ul><ul><ul><li>or </li></ul></ul><ul><ul><li>1.00 meter = 10.0 decimeters = 100. centimeters </li></ul></ul>Converting Units (multiply method) Converting Units (decimal method) milli centi deci meter liter gram deca hecto kilo
    15. 15. <ul><li>Now let’s try our previous example from meters to kilometers: </li></ul><ul><ul><li>16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers </li></ul></ul><ul><li>So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left ( the same direction as in the diagram below ) </li></ul>milli centi deci meter liter gram deca hecto kilo
    16. 16. <ul><li>If you move to the left in the diagram, move the decimal to the left </li></ul><ul><li>If you move to the right in the diagram, move the decimal to the right </li></ul>milli centi deci meter liter gram deca hecto kilo
    17. 17. Another Example <ul><li>Now let’s start from centimeters and convert to kilometers </li></ul><ul><ul><li>400,000 centimeters = 4.00000 kilometers </li></ul></ul><ul><ul><li>OR 4 km </li></ul></ul>milli centi deci meter liter gram deca hecto kilo
    18. 18. More Practice <ul><li>Now let’s start from meters and convert to centimeters </li></ul><ul><ul><li>5 meters = 500 centimeters </li></ul></ul><ul><li>Now let’s start from kilometers and convert to meters </li></ul><ul><ul><li>.3 kilometers = 300 meters </li></ul></ul>milli centi deci meter liter gram deca hecto kilo milli centi deci meter liter gram deca hecto kilo
    19. 19. Metric System Summary <ul><li>Base units are meter (length), liter (volume) & gram (weight/mass) </li></ul><ul><li>Metric system is based on powers of 10 </li></ul><ul><ul><li>For conversions within the metric system, each “step” is 1 decimal place to the right or left </li></ul></ul><ul><ul><ul><li>Using the diagram below, converting to the right, moves the decimal to the right and vice versa </li></ul></ul></ul>milli centi deci meter liter gram deca hecto kilo
    20. 20. Careers in Science <ul><li>Top 10 highest paying Bachelor Degrees for 2011 </li></ul><ul><ul><li>10 - Software Engineering (mid-career salary of $97,600) </li></ul></ul><ul><ul><li>9 - Industrial Engineering </li></ul></ul><ul><ul><li>8 - Mechanical Engineering </li></ul></ul><ul><ul><li>7 - Materials Science and Engineering </li></ul></ul><ul><ul><li>6 - Aerospace/Aeronautical Engineering </li></ul></ul><ul><ul><li>5 - Electrical Engineering (mid-career salary of $104,000) </li></ul></ul><ul><ul><li>4 - Computer Engineering </li></ul></ul><ul><ul><li>3 - Nuclear Engineering </li></ul></ul><ul><ul><li>2 - Chemical Engineering </li></ul></ul><ul><ul><li>1 - Petroleum Engineering (mid-career salary of $157,000) </li></ul></ul><ul><li>All of these are degrees within the field of Physics! </li></ul>
    21. 21. Converting English to Metric Units <ul><li>U.S. is one of the few countries using the &quot;English&quot; or &quot;Standard&quot; unit system </li></ul><ul><ul><li>inches/feet/yards (length) </li></ul></ul><ul><ul><li>cups/quarts/gallons (volume) </li></ul></ul><ul><ul><li>ounces/pounds (weight/mass) </li></ul></ul><ul><li>SI (Systém Internationale) units are mostly Metric and NEVER English units </li></ul><ul><li>Helpful for international travel </li></ul><ul><li>Essential for careers in science </li></ul>
    22. 22. <ul><li>The “Factor-Label” Method </li></ul><ul><ul><li>Units, or “labels” are canceled, or “factored” out </li></ul></ul><ul><ul><li>Example: convert yards to meters </li></ul></ul>Using Dimensional Analysis to Convert English to Metric Units Multiply by the conversion factor meter yards x yards = meters Start with what you know Units cancel out
    23. 23. Common English to Metric 1 liter = 1.057 quarts 1.057 qt/L or 1 L/1.057 qt or 0.946 L/qt 1 kilogram = 2.2 pounds 2.2 lb/kg or 1 kg/2.2 lb or 0.454 kg/lb 1 meter = 1.094 yards 1.094 yd/m or 1m/1.094 yd or 0.917m/yd 1 inch = 2.54 cm 2.54 cm/inch or 1 in/2.54 cm Conversion Factors
    24. 24. Dimensional Analysis <ul><li>Steps: </li></ul><ul><ul><li>1. Identify starting & ending units. </li></ul></ul><ul><ul><li>2. Line up conversion factors so units cancel. </li></ul></ul><ul><ul><li>3. Multiply all top numbers & divide by each bottom number. </li></ul></ul><ul><ul><li>4. Check units & answer. </li></ul></ul>1 meter 1.094 yards x 5 yards = ? meters 1 1 5 x 1m 1.094 = 4.57 meters 3 2 4