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Description
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 Prefix
Symbol
Factor
S.N.
Example
giga
G
1 000 000 000
109
Gigameter (Gm)
mega
M
1 000 000
106
Megagram (Mg)
kilo
k
1 000
103
Kilometer (km)
deci
d
1/10
10-1
Deciliter (dL)
centi
c
1/100
10-2
Centimeter (cm)
milli
m
1/1000
10-3
Milligram (mg)
micro
µ
1/1 000 000
10-6
Microgram (µg)
nano
n
1/1 000 000 000
10-9
Nanometer (nm)
pico
p
1/1 000 000 000 000
10-12
Picometer (pm)
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 2.54 cm
OR
2.54 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 2.54 cm
=
7.01 in.
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???
