The Metric System

Units, Definitions and History

History

The disparate measurement system was one of the most frequent causes of disputes amongst merchants and between citizens and tax collectors across Europe.

Leaders of the French revolutionary governments decided a new system was need.

1791: first official adoption of a universal measuring system.

1799: final proclamation of metric system placed in the Archives of the Republic.

Today, 95% of the world’s population live in metricated countiries.

SI Units

Seven base units in SI Time (second) Length (meter) Mass (kilogram) Temperature (Kelvin) Amount of a substance (mol) Electric current (ampere) Luminous intensity (candela)

SI Units Cont.

Derived units in SI Volume: derived unit is the cubic

meter (m3); cubic centimeter is more commonly used (cm3). For liquids, the liter is used; 1 L = 1 dm3.

Density: ratio that compares the mass of an object to its volume. The units for density are often expressed as g/cm3

Prefixes Used with SI Units

Picometer (pm)10-121/1 000 000 000 000ppico

Nanometer (nm)10-91/1 000 000 000nnano

Microgram (µg)10-61/1 000 000µmicro

Milligram (mg)10-31/1000mmilli

Centimeter (cm)10-21/100ccenti

Deciliter (dL)10-11/10ddeci

Kilometer (km)1031 000kkilo

Megagram (Mg)1061 000 000Mmega

Gigameter (Gm)1091 000 000 000Ggiga

ExampleS.N.FactorSymbolPrefix

Dimensional Analysis

A technique for converting from one unit to another

Conversions WITHIN the Metric System

You can simply move the decimal point... But you have to know how to move it!!

Metric Unit Conversions

Metric Unit Conversions

Use this to remember the metric prefixes:

“King Henry Died By Drinking Chocolate Milk

The first letters represent the prefixes (kilo, hecto, deca, base, deci, centi, milli)

Example

It is common for runners to do a “10K” run. This means they are running 10 kilometers. How many millimeters is that?

A lot!!!

Answer

Look at the staircase graphic... Start on the prefix “kilo” Move down the staircase 6 steps (don't

count the step you start on) to get to the prefix “milli”

This means you move the decimal point 6 places to the RIGHT

10 km is converted to 10,000,000 mm

Beyond the Metric System

If you need to convert to or from units that are NOT metric units, we use a unit conversion technique called... “dimensional analysis”

D.A.

Conversion Factors

In dimensional analysis, we make conversion factors into fractions that we will multiply by. For example, one conversion factor is:

1 inch = 2.54 cm We can make two fractions out of this...

1 inch OR 2.54 cm2.54 cm 1 inch

Example

A pencil is 17.8 cm long, what is its length in inches? Start with the “given”: 17.8 cm Multiply by the “conversion factor”

17.8 cm x 1 inch = 2.54 cm

Example

A pencil is 17.8 cm long, what is its length in inches? Cross cancel “like” units:

17.8 cm x 1 inch = 2.54 cm

Example

A pencil is 17.8 cm long, what is its length in inches? Do the math using the correct number of

significant figures (based on given information)

17.8 cm x 1 inch = 7.01 in. 2.54 cm

Which number goes on top and bottom in the conversion factor?

Usually...

The unit you WANT goes on TOP

The unit you want to CANCEL goes on BOTTOM

Example

A pencil is 8.1 inches, how many cm is it?

8.1 inches x 2.54 cm = 21 cm 1 inch

The unit we WANT is cm so we put 2.54 cm on TOP of the conversion

factor.

Multi-Step Example

Sometimes, we must “string” several conversion factors together to get from one unit to another. Ex. Mrs. DeLong's class is 47 minutes

long. How many days long is this???

Multi-Step Example

Need to go from minutes to hours to days

47 min x 1 hr x 1 day = 60 min 24 hrs

Notice how “like” units can be cross-canceled.

Multi-Step Example

Need to go from minutes to hours to days

47 min x 1 hr x 1 day = 0.033 days60 min 24 hrs

Notice how “like” units can be cross-canceled.