Measuring Matter
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This document discusses measuring systems and converting between units. It covers: - The English and metric systems, including their base units and scales. - The metric system is decimal-based while English uses various units. - Methods for converting between units like meters to centimeters using prefixes and multiplication. - Examples are provided for converting distances, volumes, and temperatures between English and metric units.
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Measuring Matter
- 1. Measuring Matter (and converting units)
- 3. English units – base 4 Metric Units – base 10 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
- 4. Metric System Units • Base units for different measurements • Length = meter (SI = m) • Volume = liter (SI = m3 ) • Weight (Mass) = gram (SI = kg) • Temperature = degrees Celsius (SI = K)
- 5. Metric System • Scale is based on powers of ten: – kilo (1000) – centi (1/100) – milli (1/1000) kilo hecto deca Base Units meter gram liter deci centi milli 1000 100 10 1 0.1 0.01 0.001
- 6. • meter is the base unit for length – Length of a tree branch • 1.5 meters – Length of a room • 5 - 10 meters – Length of a ball of twine stretched out • 25 - 50 meters
- 7. • What about a longer distance, like from your house to school? – Let’s say you live 10 miles from school • 10 miles = 16093 meters – 16093 is a big number – what if you could add a prefix onto the base unit to make it easier to manage? • 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)
- 8. • For each “step” to the right, you move the decimal in the same direction Example: change meters to centimeters 1 meter = 10 decimeters = 100 centimeters or 1.00 meter = 10.0 decimeters = 100. centimeters kilo hecto deca meter liter gram deci centi milli Converting Units (multiply method) Converting Units (decimal method)
- 9. Another Example • Now let’s start from centimeters and convert to kilometers 400,000 centimeters = 4.00000 kilometers OR 4 km kilo hecto deca meter liter gram deci centi milli
- 10. More Practice • Now let’s start from meters and convert to centimeters 5 meters = 500 centimeters kilo hecto deca meter liter gram deci centi milli kilo hecto deca meter liter gram deci centi milli • Now let’s start from kilometers and convert to meters .3 kilometers = 300 meters
- 11. Experiment 23.1 Measuring Matter (ME!) Type of Measure English Units Metric Units How tall are you? Length inches cm How high can you jump? How much do you weigh? Mass pounds kg How strong is your hair? For how long can you jump on one leg? Time min/sec s How fast can you do 10 jumping jacks? How much air do your lungs hold? Volume gallons l How much can you swallow in one gulp? How warm is it inside your ear? Temp. 0 F 0 C How warm is the palm of your hand?
- 12. English Units • The U.S. is one of only a few countries using the "English Standard" or “customary” unit system – inches/feet/yards (length) – cups/quarts/gallons (volume) – ounces/pounds (weight/mass) – Fahrenheit (temperature)
- 13. • The “Factor-Label” Method – Units are canceled or “factored” out Example: convert yards to meters Using Dimensional Analysis to Convert English to Metric Units meter yards xyards = meters Start with what you know Multiply by the conversion factor What unit you’re trying to get to
- 14. Why Conversion Factors Work • 5 x 2 = 5 x 1 = 2 • 3 x 0.7 = 3 x 1 = 0.7 • 6 x 0.5 = 6 x 1 = ½ 5 3 6 • 4 ft x 12 in = 1 ft • 150cm x 1m = 100 cm • 2 m x 1 yd = 0.9 m 48 in 1.5m 2.2 yd
- 16. Dimensional Analysis • Steps: 1. Identify begining & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units. 1 meter 1.1 yards x5 yards = ? meters 1 1 2 5 x 1m 1.1 = 4.54 meters 3 4 4.56 m Convert 5 yards into meters.
Editor's Notes
- 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
- Materials: measuring tapes, bathroom scale, spring scales, oscilloscope, stopwatch/timers, graduated cylinders, tennis ball, thermometer, balloons Other measuring activities: How big is your head? How far can you throw a tennis ball? What is the highest and lowest pitch you can sing? How far apart are your ears?