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Topics Metric System Conversions Dimensional Analysis

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If you show a good knowledge of the English measurement system, you can skip all test questions related to the metric system.

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If these are one quart each, how many gallons are here?

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Strawberries and other fruits are often sold in one quart containers. Are these quarts the same size as a quart of strawberry juice?

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What does 8 quarts of strawberries make?

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An ounce of prevention is worth a pound of cure. How many ounces of gold does it take to make a pound? This is a cap from a RC cola bottle? How much does the RC cola weigh? These are 16 oz gloves. How many pounds do each weigh? The standard (Avoirdupois) pound of the United States is equivalent to the weight of cubic inches of distilled water at 62 o Fahrenheit, the barometer being at 30 inches, and the water weighed in the air with brass weights. 12 troy ounces make 1 troy pound=.823 lbs avoirdupois

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Apothecary System used in medicine Based on the weight of one grain of wheat. 20 grains make a scruple 3 scruples make a dram 8 drams make a ounce 12 ounces make a pound (troy pound)

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Dec. 11, 1998

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Sept. 23, 1999

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The loss of the the Mars Climate Orbiter on September 23, 1999, was a most unfortunate and highly avoidable event. The cause of the mishap has been traced to a mix-up over units. Preliminary findings indicated that one team used English units (e.g., inches, feet and pounds) while the other used metric units for maneuvers required to place the spacecraft in the proper Mars orbit. The 'root cause' of the loss of the spacecraft was the failed translation of English units into metric units. For nearly three centuries, engineers and scientists have been struggling with English units. The loss of the the Mars Climate Orbiter on September 23, 1999, was a most unfortunate and highly avoidable event. The cause of the mishap has been traced to a mix-up over units. Preliminary findings indicated that one team used English units (e.g., inches, feet and pounds) while the other used metric units for maneuvers required to place the spacecraft in the proper Mars orbit. The 'root cause' of the loss of the spacecraft was the failed translation of English units into metric units. For nearly three centuries, engineers and scientists have been struggling with English units.

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In weightlessness 454 grams is still 454 grams; however, 1 pound will be zero pounds in zero gravity. What is the English unit for mass? In the English system the unit for mass is the slug. One slug sitting in Earths gravity has the weight of 32 pounds.

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Newtons second law of motion f = 1 slug x 32 ft/sec per sec (22 mph per sec) 1 lb = ? slugs x 32 ft/sec per sec 32 lbs = 1 slug x 32 ft/sec 2 2 bowling balls have the mass of 1 slug.

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Weight versus Mass

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Something has mass if it is affected by gravity. These methods wont work in the weightlessness of space.

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If the girls push with the same strength, one can measure the distance the two cars moved after 5 seconds and calculate mass. On level ground, gravity has no effect on the difficulty of overcoming the mass of the cars.

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Air conditioner rated at 18,000 BTU per hour. What does BTU stand for and what does it measure? British Thermal Units = Energy to raise or lower 1 pound of water 1 degree Fahrenheit

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Seabiscuits races like most horse races goes for 10 furlongs. How far is that?

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What if gallons were different sizes in different cities?

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What if clothing sizes were different in different cities?

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In his first annual message to Congress (1790 January), President George Washington pressed for uniformity in currency, weights, and measures. Secretary of State Thomas Jefferson urged Congress to reduce the existing separate systems of dry and liquid measures to one set of measures. Over 200 years later, we still have separate systems. For example, our dry quart is larger than our liquid quart, so four cups of flour and 4 cups of milk should be measured with separate measuring devices-which differ in size! Jefferson's second plan put before Congress was to reduce every branch [of measurement] to the same decimal ratio already established for coin, and thus bring the calculations of the principal affairs of life within the arithmetic of every man who can multiply and divide plain numbers. Congress took no action. Washington urged action again in his second annual message to Congress (1790 December 08) and the House referred the matter to the Senate, whose committee in this matter declined (1791 March 01) due to negotiations in progress with the French and British Governments to obtain an international standards of measurements.

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Currency is based on 10.

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In the same year of 1790 King Louis XVI of France was also weary of the inconsistencies of measurement that was hurting trade. He ordered a new system of measurements be developed.

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Earlier in that century, Fahrenheit and Celsius used water as the basis of their thermometers. Their thermometers were calibrated using water, which everyone had access to. This made their thermometers useful.

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Everyone has access to the Earth, so this new system was to be based on the size of the Earth. The idea was to measure a part of Earths surface over a few degrees, then calculate distance from Equator to North Pole.

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A survey team was suppose to measure the distance between Barcelona, Spain going through Paris and up to the English Channel.

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By dividing the distance from the equator to the north pole by 10 million, a convenient length was defined. It was a little longer than a yard, and the name would be from the Greek word, Metron, meaning to measure. 10,000,000 Equator to North Pole

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The motto for the metric system was: For all people, for all time

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Based on 10 & using Arabic Numerals Since the number system in use was no longer Roman Numerals, but the decimal number system borrowed from the Arab worlds and from India, the measurement system should also be based on 10 to make conversions easy.

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Since we have 10 fingers, a number system based on 10 was developed.

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Place Value Roman Numerals did not take advantage of place value. X in Roman Numerals meant ten. XXX meant thirty. It didnt matter where the X was placed; it always had the value of 10

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Modern number systems use place value. In other words, a numeral has a different value depending where its placed.

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4/20/ versus 5

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Multiplying & Dividing by 10 Because of place value, we can multiply by ten by moving all digits to the left (or you can look at it as the decimal point moving to the right.) 25. x 10 = 250. Dividing by 10 is just the reverse.

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Decimal The word decimal from from Latin decimalis meaning of a tithe A tithe was traditionally one tenth of income, so deci- meant one tenth. The new measuring system should also be based on tens and tenths.

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Cubits Yards Miles Nautical Miles Feet Hands Inches Leagues Chains Furlongs

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sq. miles sq. yards sq. ft. sq. in. acres

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Barrel Cubic inches Cubic feet Cubic yards Minims Drops Gallons, imperial gallons, quarts, pints, fluid ounces, pecks, bushels

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1 gram defined as the mass of one cubic centimeter of water (or one milliliter [mL] of water_.

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Liter from Litron: Measure of capacity One liter of water has a mass of one kilogram

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Force Push one kilogram pushed to so that it reaches the speed of one meter per second. Newton

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You are not changing the size, just the name.

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Convert 0.15 meters to centimeters 0.15 meters = centimeters Starting amount End Amount.01 1 centi 0.15 meters = 15 meters 100 = 15 centimeters If saying 15 hundredths, just say 15 centi- equal

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Convert 5234 millimeters to meters 5234 millimeters = meters Starting amount End Amount milli millimeters 5234 meters 1000 equal

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Convert 5234 millimeters to centimeters 5234 millimeters = centimeters Starting amount End Amount milli millimeters equal 0.01 centi centimeters

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Convert 5234 millimeters to inches 5234 millimeters = inches Starting amount End Amount milli equal 0.01 centi 2.54 cm 1 inch 1 inch 2.54 cm

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I wonder how many pennies are in 1 mega buck?

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= cents 1 M$ 1 x 10 8 Units Match!

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Convert 21 grams per liter (21 g/L) to milligrams per milliliter (mg/mL) 21 grams Liter = mg mL Starting amount End Amount milli equal milli

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Convert 21 mg per liter (21 g/L) to grams per 100 cc 21 mg Liter = g 100cc Starting amount End Amount milli equal 1L 1000cc 0.1 equal

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mega-Mmillion1,000, kilo-kthousand1, kilograms deci-dtenth1/10 = dm 3 =liter centi-chundredth1/100 = cm=centimeter cc=cubic cm milli-mthousandth1/1000 = mg=milligram mL=milliliter micro-µmillionth1/1,000,000 = µg=microgram nano-nbillionth 1/1,000,000,000 = nm=nanometers Examples Metric facts: 1 cubic centimeter = 1 milliliter (1 cc=1mL) Liter = 1 cubic decimeter = 1,000 cubic centimeters = 1,000 milliliters Lower case m stands for meter or milli. Capital L for liter.

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