You, Me, And The Metric System!
Measure by TEN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
How Do Metric Values Relate?
METRIC RELATES... In 10!
Simply divide 1 m
(meter) in exactly 10
parts,
each of which measures
10 cm (centimeters).
Then make a cube
container that is
10 cm x 10 cm x 10 cm
(1000 cm³)
that we can fill with
water.
And like magic, when you
fill this cube container
with water, it has the
volume of exactly 1 L
(liter).
ALL SIMPLY RELATED IN 10.
But then, when you place this
cube filled with water on a scale
it has a mass of exactly 1 kg
(kilogram).
How about that?
length, volume and mass,
all simply related in 10.
Now YOU TOO can say mass.
Just remember that for everyday
purposes you will begin to appreciate
the close relationship between
length of 1 m (meter),
volume of 1 L (liter) and mass of 1 kg
(kilogram).
For more metric fun visit;
http://www.metricamerica.com/index.htm
SI Base Units
Name
Symbol
Unit of
meter
m
length
kilogram
kg
mass
second
s
time
ampere
A
electric current
Kelvin
K
thermodynamic
temperature
mol
amount of substance
cd
luminous intensity
mole
candela
SI Derived Units
Equivalent in
Base Units
Other Equivalents
activity (of a radionuclide)
1/s
-
C
quantity of electricity, electric charge
A·s
F·V = J/V
degree
Celsius
°C
Celsius temperature
K
K – 273.15
farad
F
capacitance
A²·s4/kg·m²
C/V=A·s/V
gray
Gy
absorbed dose, specific energy
imparted, kerma
m²/s²
J/kg
henry
H
inductance
kg·m²/A²· s²
Wb/A = V·s/A
hertz
Hz
frequency
1/s
-
joule
J
kg·m²/s²
N·m = W·s = Pa·m³
katal
kat
catalytic activity
mol/s
-
lumen
lm
luminous flux
cd
cd·(4·π sr) = lx·m²
Name
Symbol
becquerel
Bq
coulomb
Unit of
energy, work, quantity of heat
Name
Symbol
Unit of
newton
N
force
ohm
W
electric resistance
pascal
Pa
pressure, stress
radian
rad
plane angle
siemens
S
electric conductance
sievert
Sv
dose equivalent
steradia
n
sr
solid angle
tesla
T
magnetic flux density
volt
V
electric potential difference,
electromotive force
watt
W
power, radiant flux
weber
Wb
magnetic flux
Equivalent in
Base Units
Other
Equivalents
kg·m/s²
J/m = W·s/m =
Pa·m²
kg·m²/A²·s³
V/A = 1/S
kg/m·s²
N/m² = J/m³
1
1/(2·p) of a
circle
A²·s³/kg·m²
A/V = 1/W
m²/s²
J/kg
1
1/(4·p) of a
sphere
kg/A·s²
Wb/m² =
N/A·m
kg·m²/A·s³
W/A = J/C =
Wb/s
kg·m²/s³
J/s = V·A =
N·m/s
kg·m²/A·s²
V·s = H·A =
T·m² = J/A
The Prefixes of the SI
yotta [Y]
1 000 000 000 000 000 000 000 000
1 000 000 000 000 000 000 000
= 1024
(one
septillion)
= 1021
(one
sextillion)
= 1018
(one
quintillion)
= 1015
(one
quadrillion)
zetta
[Z]
exa
[E]
peta
[P]
tera
[T] 1 000 000 000 000
= 1012
(one trillion)
giga
[G] 1 000 000 000
= 109
(one billion)
mega
[M 1 000 000
]
= 106
(one million)
= 103
(one
thousand)
= 100
(one)
kilo
[k]
1 000 000 000 000 000 000
1 000 000 000 000 000
1 000
1
The Prefixes of the SI
milli
[m]
micro
[m]
nano
[n]
pico
[p]
0.001
0.000 001
0.000 000 001
0.000 000 000 001
= 10-3
(one
thousandth)
= 10-6
(one
millionth)
= 10-9
(one
billionth)
= 10-12
(one
trillionth)
= 10-15
(one
quadrilliont
h)
= 10-18
(one
quintilliont
h)
= 10-21
(one
sextillionth)
= 10-24
(one
septillionth)
0.000 000 000 000 001
femto
[f]
0.000 000 000 000 000 001
atto
[a]
zepto
[z]
yocto
[y]
0.000 000 000 000 000 000 001
0.000 000 000 000 000 000 000 001
All the previous SI prefixes are multiples
or sub-multiples of 1 000. The usage of
the four SI prefixes below is by custom
limited to non-technical measurements
of length, area and volume.
A. H.
B.
C.
D.
E.
F.
G.
hecto
[h]
100
= 102
(one hundred)
deca
[da]
10
= 101
(ten)
1
= 100
(one)
deci
[d]
0.1
= 10-1
(one tenth)
centi
[c]
0.01
= 10-2
(one hundredth)
Some Common Conversions
Length and Area:
1 foot = 12 inches
1 mile = 5,280 feet
1 kilometer = 1,000 meters
1 mile ≈ 1.6 kilometers
1 foot ≈ 0.305 meter
1 yard = 3 feet
1 mile = 1,760 yards
1 meter = 1,000 millimeters
1 inch ≈ 2.540 centimeters
1 acre = 4,840 square yards
1 square yard = 9 square feet
1 square foot = 144 square inches
Volume:
1 gallon = 4 quarts
1 gallon ≈ 231 cubic inches
1 liter = 1,000 milliliters
1 liter ≈ 1.057 quarts
1 gallon ≈ 3.785 liters
1 quart = 2 pints
1 pint = 16 fluid ounces
1 cubic yard = 27 cubic feet
1 cubic foot ≈ 7.48 gallons
Weight (on Earth’s surface)
1 ton = 2,000 pounds
1 kilogram ≈ 2.205 pounds
1 pound = 16 ounces
1 pound ≈ 0.454 kilogram
1 kilogram = 1,000 grams
Converting from One Metric Unit to Another
Skills you need to do this include:
1) memorize the metric prefixes names and symbols
2) determine which of two prefixes represents a larger amount
3) determine the exponential "distance" between two prefixes
4) significant figure rules
5) scientific notation
The key skill in solving these problems is to construct a
conversion factor. This conversion factor will make the
old unit go away and create the new unit in its place.
Along with this change, there will be a change in the
value of the number.
Convert 2.50 mg to picograms
DIMENSIONAL ANALYSIS:
STEP ONE: Write the value (and its unit) from the
problem, then in order write: 1) a multiplication sign, 2)
a fraction bar, 3) an equals sign, and 4) the unit in the
answer. Put a gap between 3 and 4. All that looks like
this:
The fraction bar will have the conversion factor. There
will be a number and a unit in the numerator and the
denominator
STEP TWO: Write the unit from the problem in the
denominator of the conversion factor, like this:
STEP THREE: Write the unit expected in the
answer in the numerator of the conversion factor.
STEP FOUR: Examine the two prefixes in the conversion
factor. In front of the LARGER one, put a one.
STEP FIVE: Determine the absolute distance
between the two prefixes in the conversion unit.
Write it as a positive exponent in front of the other
prefix
Now, multiply and put into proper scientific notation
format. Don't forget to write the new unit.
Here are all five steps for the
second example, put into one
image:
Why a one in front of the larger unit? I believe it is easier
to visualize how many small parts make up one bigger part,
like 1000 m make up one km
Two Comments
1) If you do the conversion correctly, the
numerical part and the unit will go in
opposite directions. If the unit goes from
smaller (mm) to larger (km), then the
numerical part goes from larger to smaller.
There will never be a correct case where
number and unit both go larger or both go
smaller.
2) A common mistake is to put the one in
front of the SMALLER unit. This results in
a wrong answer. Put the one in front of the
LARGER unit.
Cross this line
move decimal by 3
for each step.
Cross this line
move decimal by 3
for each step.
Step Method
Mega
Kilo
Hecto
Deka
Base
Deci
Centi
Milli
Micro
Nano
pico
Move
only one
decimal
for
each
step in
this area
Going up,
the
decimal
moves to
the left
for each
step
Going
down,
decimal
moves to
the right
for each
step
Practice Problems
1. 0.75 kg to milligrams
2. 1500 millimeters to km
3. 2390 g to kg
4. 0.52 km to meters
5. 65 kg to g
6. 750 micrograms to g
7. 0.25 megameters to cm
8. 23.8 ng to kg
9. 2.77 kg to mg
10. 2.90 cm to picometers
11. 45.6 microliters to megaliters
12. 1.08 kg to mg
13. 9.57 x 10-8 mm to nanometers
14. 2.00 L to mL
15. 35.28 mL to L
Team competition!
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
L.
M.
N.
O.
For your review try;
http://www.aaamath.com/mea.html