The Metric System

Base UnitsPrefixes

Thinking in MetricTemperature

TimeMass, Volume, Density

SI

•Systéme International d'Unités.

• The other name for the metric system.

History of the Metric System

Created at the end of the 18th Century to provide a consistent system of units amidst a wide variety of different standards.

Previously, each area had its own units inherited from earlier times.

Not reproducable, not standarde.g., a "cubit" was the length from the

elbow to the tip of the middle finger.e.g., a rundlet was worth 16 gallons in a

certain town and 18 gallons in another town

History of the Metric System

The metric system became compulsory in France on Dec.10, 1799 (Napoleon was First Consul) and, being practical, spread slowly across Europe.

Not without resistance : a few years later, even France came back to the old system for several years. Japan made it official in 1868 and Russia in 1917.

England was the last European country to adopt it : the adaptation period began in 1965 and was to end officially in 1980.

History of the Metric System

The seven primary units are now :

* length : meter (m) * mass : kilogram (kg) * time : second (s) * electric current : ampere (A) * temperature : Kelvin or Celsius (K or °C) * quantity of matter : mole * light intensity : candela (cd)

USA and the Metric System

Thomas Jefferson considered a conversion to the metric system. In 1889, the US Congress adopted the meter as a standard and, thereafter, the inch, foot, yard, etc. were defined in relation to the meter.

The Metric Conversion Act of 1975 committed the US to the increasing use of, and voluntary conversion to, the metric system of measurement.

SI Base Units of Measurement

• Mass– the gram; g

• 1 gram ≈ 1/28 ounce

• Length– the meter; m

• 1 meter ≈ 1.094 yard

• Volume– the liter; l

• defined as 1000 cubic centimeters• 1 liter ≈ 1.057 quart

Metric System

• The metric system is based on a base unit that corresponds to a certain kind of measurement

• Length = meter• Volume = liter• Weight (Mass) = gram

• Prefixes plus base units make up the metric system – Example:

• Centi + meter = Centimeter• Kilo + liter = Kiloliter

Metric System

kilo hecto deca

Base UnitsMete

rLiterGram

deci centi milli

Kilo (k) meter (m) Deci (d)Hecto (h) liter (L) Centi (c)Deca (da) gram (g) Milli (m)

The Metric Stairs• Kilo – 1000• Hecto – 100• Deka – 10• Base Units – 1• Deci – 1/10• Centi – 1/100• Milli – 1/1,000

• Micro – 1/1,000,000• Nano –

1/1,000,000,000Base Units =Meter, Liter, Gram

One of the clever ideas behind the system was to use only multiples of ten.

Metric System• Since prefixes are based on powers of 10. What

does this mean to us?

– From each prefix every “step” is either:• 10 times larger

or• 10 times smaller

– For example• Centimeters are 10 times larger than

millimeters• 1 centimeter = 10 millimeters

Length

• Length is the distance between two points.

• The SI base unit for length is the meter.

• We use rulers or meter sticks to find the length of objects.

Mass• Mass is the amount of matter that makes

up an object.• A golf ball and a ping pong ball are the

same size, but the golf ball has a lot more matter in it. So the golf ball will have more mass.

• The SI unit for mass is the gram.• A paper clip has a mass of about one gram.• The mass of an object will not change

unless we add or subtract matter from it.

Kilogram

As the name implies, the original unit was the gram (weight of 1 cubic centimeter or 1 milliliter of water at 4 °C) but it soon became the kg (or 1000 grams or one cubic decimeter of water), and defined by its model in platinum-iridium kept in Paris.

One may also mention the carat used in jewelry (5 carats = 1 gram). But carat is not an SI unit!

Measuring Mass• We will use a triple beam balance scale

to measure mass.

Mass vs- Weight• Gravity pulls equally on both sides of a

balance scale, so you will get the same mass no matter what planet you are on.

Measuring Weight and Forces

• A force is a push or a pull.

• The SI unit for force is the Newton (N).

• Spring scales will be used to measure forces.

• Since weight is the force of gravity acting on objects, we will use the Newton for weight also.

Weight

• Weight is a measure of the force of gravity on an object.

• Your weight can change depending on the force of gravity. The gravity will change depending on the planet you are on.

• The SI unit for weight is the Newton (N).• The English unit for weight is the pound.

Gravity

• Gravity is the force of attraction between any two objects with mass.

• The force depends on two things:• more distance = less gravity = less weight• less distance = more gravity = more weight• more mass = more gravity = more weight• less mass = less gravity = less weight

Weight and MassEarth

1 gravity

Moon

1/6th gravity

Jupiter

2.5 gravities

On orbit

0 gravity

Jill’s mass

30kg 30kg 30kg 30kg

Jill’s weight

300N 50N 750N 0 newtons

• Notice that Jill’s mass never changes. Her mother will not allow us to take parts off her, or add parts to her, so her mass stays the same. Jill is 30kg of little girl no matter where she goes!

Volume• Volume is the

amount of space contained in an object.

• We can find the volume of box shapes by the formula Volume = length x width x height

• In this case the units would be cubic centimeters (cm3).

• So a box 2 cm x 3 cm x 5cm would have a volume of 30 cm3

Liquid Volume

• When the metric system was created, they decided that 1 cm3 of water would equal 1 milliliter of water and the 1 mL of water will have a mass of one gram.

• 1 cm3 of anything = 1 mL of anything• 1 cm3 water = 1 mL of water = 1

gram

Water Displacement: Finding the volume of an irregular shaped

object• We can use water

displacement to find the volume of objects that are not boxed shaped.

• We can put 50-mL of water in a graduated cylinder. If a rock causes the level to rise to 73-mL, the the rock must have a volume of 23-mL.

Water Mass and Volume

• 1 cm3 water = 1 mL of water = 1 gram• So what would be the mass of 50 mL of

water be?• 50 grams• So what would be the mass of 1 liter of

water be?• 1 L = 1000 mL so its mass would be

1000 grams or a kilogram.

Time

Unit of time: second

The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Celsius: The Metric Temperature Scale

• Also called the centigrade scale.• Definitions

– 0 Celsius = 32 Fahrenheit = water freezes

– 100 Celsius = 212 Fahrenheit = water boils

– Therefore, 1C = 1.8F

• Conversions Celsius = 5/9 x ( Fahrenheit - 32) Fahrenheit = (9/5 x Celsius) + 32

0C

100C

32F

212F

History of Temperature Scales

The first to seal mercury in a glass rod was Daniel Fahrenheit in Germany (1709). He had to build a scale from scrap : zero was allocated to the temperature of a salty mixture, assuming that nothing could ever be colder and 96 was his estimate of the human body. With such a scale, water would freeze at 32 and boil at 212.

1686 - 1736

History of Temperature Scales

In 1730, in France, Rene Antoine Ferchault de Reaumur built the first alcohol thermometer. He allocated 0 to freezing water and 80 to boiling water.

In 1742, in Sweden, the astronomer Anders Celsius used a scale allocating 100 to freezing water and 0 (!) to boiling water. His scale was later inverted (0 to freezing water and 100 for boiling) and long known as "centigrade".

CelsiusCelsius1701 - 17441701 - 1744

History of Temperature ScalesComparing the scales, 9° Fahrenheit = 5° Celsius

* C = (F - 32) * 5/9 * F = 32 + C * 9/5

The two scales meet at - 40

* - 40°F is the same as - 40°C

Absolute Temperature Starting from the absolute zero (at -273.15 C or -459.67 F), it was tempting to follow the old idea of Fahrenheit and have only a positive scale. This was done by Sir William Thomson, Lord Kelvin, from the Celsius scale.

Water is freezing at 273.15 K, and boiling at 373.15 K

The SI uses the Kelvin scale, defined by the triple point of water (at 273.16 K or 0.01°C) and absolute zero.

1824 - 19071824 - 1907

Density• Density is the amount of matter (mass)

compared to the amount of space (volume) the object occupies.

• We will measure mass in grams and volume in mL or cm3

Density Formula

• Density is mass divided by volume.• Density = mass/volume• Remember, all fractions are

division problems. Since the unit for mass is grams, and the unit for volume is mL or cm3, then the unit for density is g/mL, or g/ cm3

Density Formula Wheel

• Formula wheels make it easy to solve density problems.

• Cover the property you are trying to find, and do what is left over.

• To find density, cover the word density. You have mass over volume remaining. So divide mass by volume to find density!

Mass

density

volume

Density Formula Wheel

• To find mass, you cover the word mass. You now have mass times volume remaining.

• To find volume, cover volume. You have mass over density remaining, so divide mass by density to find volume.

Mass

density

volume

Understanding Density• In the following illustrations, each will

represent 1 cm3.• Each g will represent 1 gram.• Mass = 24g• Volume = 8 cm3

• Density = 3g/cm3

g g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

Understanding Densityg g g

g g g

g g g

g g g

g g g

g g g

g g g

g g g

•In other words, there are 3 grams in every cmcm33..

Conversion – The Metric Stairs

• Kilo – 1000• Hecto – 100• Deka – 10• Base Units – 1• Deci – 1/10• Centi – 1/100• Milli – 1/1,000• Micro –

1/1,000,000• Nano –

1/1,000,000,000

One of the clever ideas behind the system was to use only multiples of ten. Today mainly multiples of 1000 are in use. These are the only words to memorize

Base Units =Meter, Liter, Gram

Metric System

• 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

Metric System

• But what if you need to measure a longer distance, like from your house to school?

– Let’s say you live approximately 10 miles from school

• 10 miles = 16093 meters

– 16093 is a big number, but 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)

Metric System

– Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length

1 centimeter = 10 millimeters

Example not to scale

1 cm

40

41

41

40

1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm

Metric System• For each “step” to right,

you are multiplying by 10

• For example, let’s go from a base unit to centi

1 liter = 10 deciliters = 100 centiliters

2 grams = 20 decigrams = 200 centigrams

kilo hecto deca

meter

liter

gram

deci centi milli

( 1 x 10 = 10) = (10 x 10 = 100)

(2 x 10 = 20) = (20 x 10 = 200)

Metric System• An easy way to move within the metric system is by

moving the decimal point one place for each “step” desired

Example: change meters to centimeters

1 meter = 10 decimeters = 100 centimetersor

1.00 meter = 10.0 decimeters = 100. centimeters

kilo hecto deca

meter

liter

gram

deci centi milli

Metric System

• Now let’s try our previous example from meters to kilometers:

16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers

• 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)

kilo hecto deca

meter

liter

gram

deci centi milli

Metric System

• If you move to the left in the diagram, move the decimal to the left

• If you move to the right in the diagram, move the decimal to the right

kilo hecto deca

meter

liter

gram

deci centi milli

Metric System• Now let’s start from centimeters and convert to

kilometers

400000 centimeters = 4 kilometers

400000 centimeters = 4.00000 kilometers

kilo hecto deca

meter

liter

gram

deci centi milli

Metric System• Now let’s start from meters and convert to kilometers

4000 meters = 4 kilometers

kilo hecto deca

meter

liter

gram

deci centi milli

kilo hecto deca

meter

liter

gram

deci centi milli

• Now let’s start from centimeters and convert to meters

4000 centimeters = 40 meters

Metric System• 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

Metric System• Now let’s start from kilometers and convert to

millimeters

4 kilometers = 4000000 millimeters

or

4 kilometers = 40 hectometers = 400 decameters

= 4000 meters = 40000 decimeters

= 400000 centimeters = 4000000 millimeters

kilo hecto deca

meter

liter

gram

deci centi milli

ggmg

gmg 25.0

1000250

10001

250

Converting Between Metric Units Using Unit Factor Analysis

gmg ?250

•Multiply the unit to be converted by a conversion factor that relates the given unit of measure to the desired unit of measure.–You essentially are multiplying by one since the value above the fraction line is equal to the value below the fraction line.

•Place the value with the GIVEN unit of measure BELOW the line, and an equivalent value for the DESIRED unit of measure ABOVE the line. Then you can cancel out the given units above and below the line, leaving only the desired units.

Thinking in Metric Units of Length

• 1 kilometer– ~0.62 or ~5/8 mile

• 1 meter– 1.09 yard=39.4 inches

• 1 centimeter– ~4/10 inch

• 1 angstrom– 1/10 nm or 10-10m

• 1 mile– ~1.6 km

• 1 yard– ~0.91 m

• 1 foot– ~30.5 cm

• 1 inch– 2.54 cm or ~25 mm

Thinking in Metric Units of Volume

• 1 liter– ~1.06 quart

• 1 milliliter– 1 cubic cm (1cc)– ~"a thimble full"

• Examples– 1 teaspoon ≈ 5ml– 12 oz. soda ≈ 360 ml– 2-liter bottle of soda

• 1 gallon– ~3.8 l

• 1 quart– ~0.95 l

• 1 pint– ~0.47 l

• 1 cup– ~240 ml

• 1 fluid ounce– ~30 ml

2 liters~1/2 gal.

Thinking in Metric Units of Mass• 1 kilogram

– 2.2 pounds

• 1 gram– ~"a thimble full" of water

• Examples– 70 kg human = 154 lbs.– 1 ml of water weighs ~1

g

• 1 pound– 454 g

• 1 ounce– ~28 g

Triple Beam BalanceTriple Beam Balance

Thinking in Celsius

• -10 Celsius = frigid (14 F) • 0 Celsius = cold (32 F)• 10 Celsius = cool (50 F)• 20 Celsius = comfortably warm (68 F)• 30 Celsius = hot (86 F)• 40 Celsius = very hot (104 F)• What would you wear outside in temperatures of

--10C, 0C, 10C, 20C, 30C?

Length, Mass, & Volume • Length is the distance

between two points – measured in meters.

• Mass is the amount of matter in an object– measured in grams.

• Volume is the amount of space taken up by an object– measured in liters.

The Tools used to measure

• Length – Meter stick or ruler

• Volume – Graduated cylinder or submersion

• Mass – Triple Beam Balance or scale

Metric System

• Summary– Base units in the metric system are meter, liter,

gram– Metric system is based on powers of 10– For conversions within the metric system, each

“step” is 1 decimal place to the right or left– Using the diagram below, converting to the

right, moves the decimal to the right and vice versa

kilo hecto deca

meter

liter

gram

deci centi milli