Chapter 6Chapter 6By Tens and TenthsBy Tens and Tenths

Metric MeasurementMetric Measurement

by: Holly Baust and Chris Conoverby: Holly Baust and Chris Conover

History of MeasurementHistory of Measurement

Measure became important when humans Measure became important when humans began to trade.began to trade.– i.e. how much grain, how large a horse, how long a i.e. how much grain, how large a horse, how long a

rope, etc.rope, etc.

Units were agreed-upon and became standards Units were agreed-upon and became standards for systems of measurementfor systems of measurement– Early standards included:Early standards included:

SpanSpanPalmPalmDigit Digit FootFootCubitCubitFathomFathom

History of MeasurementHistory of Measurement

ExampleExample– Measure the width of your desk using your Measure the width of your desk using your

spanspan– Compare your span with some of your Compare your span with some of your

neighborsneighbors

DISADVANTAGES ??DISADVANTAGES ??

English System of MeasurementEnglish System of Measurement

The standards were based on a king or another The standards were based on a king or another prominent person.prominent person.King Henry IKing Henry I– YardYard

Tip of his nose to the tip of his thumb with his arm stretched Tip of his nose to the tip of his thumb with his arm stretched outoutBecame basis for English systemBecame basis for English system

– Still used in the United StatesStill used in the United States– Used almost nowhere elseUsed almost nowhere else

Disadvantages ?Disadvantages ?

History of the Metric SystemHistory of the Metric System

In 1790, Bishop Charles Maurice de In 1790, Bishop Charles Maurice de Talleyrand proposed a system.Talleyrand proposed a system.– Based on one full swing per second made by Based on one full swing per second made by

a penduluma pendulum– Rejected by the French Academy of Sciences Rejected by the French Academy of Sciences

because temperature and gravity differs because temperature and gravity differs throughout the world.throughout the world.

Instead, a system based on the length of a sea-Instead, a system based on the length of a sea-level meridian arclevel meridian arc

The MeterThe Meter

Meter : one ten-millionth of the meridian Meter : one ten-millionth of the meridian arcarc– Advantage : system is comprised of multiples Advantage : system is comprised of multiples

of powers of tenof powers of ten– Multiples of ten less than a meter are named Multiples of ten less than a meter are named

with Latin prefixeswith Latin prefixes– Multiples of ten greater than a meter are Multiples of ten greater than a meter are

named with Greek prefixesnamed with Greek prefixes

The MeterThe Meter

Nano 0.000000001 10-9

Micro 0.000001 10-6 Milli 0.001 10-3 Centi 0.01 10-2

Deci 0.1 10-1 no prefix 1.0 100 Deka 10.0 101 Hecto 100.0 102 Kilo 1000.0 103

Mega 1,000,000. 106 Giga 1,000,000,000. 109

The MeterThe Meter

How did they determine the length of the How did they determine the length of the meridian arc?meridian arc?– Instead of using the unit degree, the French Instead of using the unit degree, the French

Academy defined grade (grad) as the new unit Academy defined grade (grad) as the new unit of angular measure based on the powers of of angular measure based on the powers of ten.ten.

– 100 grades = Right Angle100 grades = Right Angle– 400 grades = Circle400 grades = Circle

Replaced grades with radiansReplaced grades with radians

Area, volume, and massArea, volume, and mass

History of the Metric SystemHistory of the Metric System

1795 : Republic of France accepted the French 1795 : Republic of France accepted the French Academy’s systemAcademy’s system1812 : Napoleon discarded this system1812 : Napoleon discarded this system1840 : Napoleon reinstated it as the mandatory 1840 : Napoleon reinstated it as the mandatory French systemFrench system1875 : 17 countries signed the Treaty of the 1875 : 17 countries signed the Treaty of the MeterMeter1960 : Meter redefined in terms of wavelength.1960 : Meter redefined in terms of wavelength.1983 : Redefined again to the distance traveled 1983 : Redefined again to the distance traveled by light inside a vacuum during a second.by light inside a vacuum during a second.

The U.S. and the Metric SystemThe U.S. and the Metric System

1866 : Made the metric system legal, but 1866 : Made the metric system legal, but not mandatory in commerce.not mandatory in commerce.1875 : Signed the Treaty of the Meter1875 : Signed the Treaty of the Meter1975 : Metric Conversion Act1975 : Metric Conversion Act– Urged voluntary conversion to the metric Urged voluntary conversion to the metric

systemsystem– Little progress was madeLittle progress was made– U.S. is one of the last to adopt the metric U.S. is one of the last to adopt the metric

system as its official measurement systemsystem as its official measurement system

Length

                                                                                                                                                                           

ActivityActivity

TimelineTimeline

1790 - Bishop Charles Maurice de Talleyrand proposed 1790 - Bishop Charles Maurice de Talleyrand proposed a system based on the length a system based on the length of a pendulum that of a pendulum that would make one full swing per second.would make one full swing per second.1795 -France officially adopted the metric system.1795 -France officially adopted the metric system.1812 -Napoleon temporarily suspended the compulsory 1812 -Napoleon temporarily suspended the compulsory provisions of the 1795 metric system adoption.provisions of the 1795 metric system adoption.1840 -The metric system reinstated as the compulsory 1840 -The metric system reinstated as the compulsory system in France.system in France.1866 - The use of the metric system made 1866 - The use of the metric system made legallegal (but not (but not mandatory) in the United mandatory) in the United States. This law also made it States. This law also made it unlawful to refuse to trade or deal in metric unlawful to refuse to trade or deal in metric quantities.quantities.

TimelineTimeline

1875 -1875 -The Convention of the The Convention of the MetreMetre signed in Paris by 17 signed in Paris by 17 nations, including the United States. The nations, including the United States. The Meter Meter ConventionConvention, , often called the often called the Treaty of the MeterTreaty of the Meter in the in the United States, United States, provided for improved metric weights and provided for improved metric weights and measures and the measures and the establishment of the establishment of the General General Conference on Weights Conference on Weights and Measures and Measures (CGPM)(CGPM) devoted to international devoted to international agreement on matters of weights agreement on matters of weights and measures.and measures.1960 -The 1960 -The metermeter was redefined in terms of wavelengths of was redefined in terms of wavelengths of light.light.1975 -The 1975 -The Metric Conversion Act of 1975Metric Conversion Act of 1975 (Public Law 94-168) (Public Law 94-168)

passed by Congress. The Metric passed by Congress. The Metric Act established the Act established the U.S. Metric BoardU.S. Metric Board to coordinate and plan the increasing to coordinate and plan the increasing use and voluntary conversion to the metric system. use and voluntary conversion to the metric system.

However, the Metric Act was devoid of any However, the Metric Act was devoid of any target dates target dates for for metric conversion. metric conversion. 1983 -The 1983 -The metermeter is redefined in terms of the speed of light. is redefined in terms of the speed of light.

Future TimelineFuture Timeline

before the end of 2009before the end of 2009 – The U.S. should allow The U.S. should allow metric-only packagingmetric-only packaging by by

amending the amending the Fair Packaging and Labeling Act (FPLA)Fair Packaging and Labeling Act (FPLA). This would be a good step towards meeting EU . This would be a good step towards meeting EU requirements for SI-only labels in 2009. requirements for SI-only labels in 2009.

2009 December 312009 December 31 – All products sold in EuropeAll products sold in Europe (with limited exceptions) (with limited exceptions)

will be required to have will be required to have only SI-metric unitsonly SI-metric units on their on their labels. Dual labeling will labels. Dual labeling will notnot be permitted. be permitted. Implementation of the labeling directive, previously Implementation of the labeling directive, previously 1999 December 311999 December 31, was extended by the , was extended by the EU EU CommissionCommission for 10 years, giving more time for for 10 years, giving more time for companies to comply and for U.S. regulations to allow companies to comply and for U.S. regulations to allow metric-only labeling on consumer products.metric-only labeling on consumer products.

Works CitedWorks Cited

Berlinghoff, William P., and Fernando Q. Gouvêa. Berlinghoff, William P., and Fernando Q. Gouvêa. Math Through the Ages: a Math Through the Ages: a Gentle History for Teachers and OthersGentle History for Teachers and Others. Farmington: Oxton House, 2002. . Farmington: Oxton House, 2002.

87-90.87-90. "Early Measurement History." "Early Measurement History." ThinkQuestThinkQuest. Oracle Education Fund. 11 Sept. . Oracle Education Fund. 11 Sept.

2006 <http://library.thinkquest.org>. 2006 <http://library.thinkquest.org>.

"Toward a Metric America." "Toward a Metric America." The National Institute of Standards and The National Institute of Standards and

TechnologyTechnology. Dec. 2003. NIST. 6 Sept. 2006 <http://www.nist.gov/metric>.. Dec. 2003. NIST. 6 Sept. 2006 <http://www.nist.gov/metric>. U.S. Metric AssociationU.S. Metric Association. 3 Sept. 2006. U.S. Metric Association. 3 Sept. 2006 . 3 Sept. 2006. U.S. Metric Association. 3 Sept. 2006

<http://lamar.colostate.edu/~hillger/#education>. <http://lamar.colostate.edu/~hillger/#education>.