# Topics Metric System Conversions Dimensional Analysis.

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Topics Metric System Conversions Dimensional Analysis

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

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

Dry Quart vs. Liquid Quart
Strawberries and other fruits are often sold in one quart containers. Are these quarts the same size as a quart of strawberry juice? Dry Quart vs. Liquid Quart Dry Quart = 1.07 Liquid Quarts

What does 8 quarts of strawberries make?
1 PECK

An ounce of prevention is worth a pound of cure.
How many ounces of gold does it take to make a pound? 12 troy ounces make 1 troy pound=.823 lbs avoirdupois 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 62o Fahrenheit, the barometer being at 30 inches, and the water weighed in the air with brass weights.

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)

MARS CLIMATE ORBITER

Dec. 11, 1998

Sept. 23, 1999

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.

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 Earth’s gravity has the weight of 32 pounds.

Newton’s second law of motion
f = ma 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/sec2 2 bowling balls have the mass of 1 slug.

Weight versus Mass

Something has mass if it is affected by gravity.
These methods won’t work in the weightlessness of space.

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

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

Seabiscuit’s races like most horse races goes for 10 furlongs
Seabiscuit’s races like most horse races goes for 10 furlongs. How far is that? 1 furlong = 1/8 mile

What if gallons were different sizes in different cities?

What if clothing sizes were different in different cities?

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. Jefferson Washington 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.

Currency is based on 10.

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.

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. Celsius Fahrenheit

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 Earth’s surface over a few degrees, then calculate distance from Equator to North Pole.

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

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

40,000,000 meters 40,000 km 1 kilometer=1,000 meters 10 million meters 10 million meters 10 million meters 10 million meters

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

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.

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

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

Modern number systems use place value
Modern number systems use place value. In other words, a numeral has a different value depending where it’s placed. 2222.0

4/20/01 0.5 versus 5

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.

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.

Metrics: Earth, water, and fingers

10 million meters 10 million meters 10 million meters 10 million meters

METER Cubits Yards Miles Nautical Miles Feet Hands Inches Leagues
Chains Furlongs METER

sq. miles sq. yards sq. ft. sq. in. acres
SQUARE METER

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

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

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

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

You are not changing the size, just the name.
CONVERSIONS You are not changing the size, just the name.

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

Convert 5234 millimeters to meters
Starting amount equal End Amount 5234 millimeters 0.001 = meters milli 5234 millimeters meters 1000

Convert 5234 millimeters to centimeters
Starting amount equal equal End Amount 5234 millimeters 0.001 centi = centimeters milli 0.01 5234. millimeters 523.4 centimeters

Convert 5234 millimeters to inches
Units match Starting amount equal equal End Amount 2.54 cm 1 inch 1 inch 2.54 cm 5234 millimeters 0.001 centi = inches milli 0.01

I wonder how many pennies are in
1 mega buck?

Units Match! 1 M\$ 1 x 108 = cents

Convert 21 grams per liter (21 g/L) to milligrams per milliliter (mg/mL)
Starting amount equal equal End Amount 21 grams Liter milli 0.001 0.001 milli = mg mL

Convert 21 mg per liter (21 g/L) to grams per 100 cc
Starting amount equal equal equal End Amount 21 mg Liter 0.001 milli 1L 1000cc = g cc

cm=centimeter cc=cubic cm milli- m thousandth 1/1000 = 0.001 10-3
Examples mega- M million 1,000,000 106 kilo- k thousand 1,000 103 kilograms deci- d tenth 1/10 = 0.1 10-1 dm3=liter centi- c hundredth 1/100 = 0.01 10-2 cm=centimeter cc=cubic cm milli- m thousandth 1/1000 = 0.001 10-3 mg=milligram mL=milliliter micro- millionth 1/1,000,000 = 10-6 µg=microgram nano- n billionth 1/1,000,000,000 = 10-9 nm=nanometers 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.