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 is10 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 appreciatethe close relationship betweenlength 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

mole mol amount of substance

candela cd luminous intensity

SI Derived Units

Name Symbol Unit ofEquivalent in

Base UnitsOther Equivalents

becquerel Bq activity (of a radionuclide) 1/s -

coulomb 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 Gyabsorbed 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 energy, work, quantity of heat 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

newton N force kg·m/s²J/m = W·s/m =

Pa·m²

ohm electric resistance kg·m²/A²·s³ V/A = 1/S

pascal Pa pressure, stress kg/m·s² N/m² = J/m³

radian rad plane angle 11/(2·) of a

circle

siemens S electric conductance A²·s³/kg·m² A/V = 1/

sievert Sv dose equivalent m²/s² J/kg

steradian

sr solid angle 11/(4·) of a

sphere

tesla T magnetic flux density kg/A·s²Wb/m² = N/A·m

volt Velectric potential difference, electromotive force

kg·m²/A·s³W/A = J/C =

Wb/s

watt W power, radiant flux kg·m²/s³J/s = V·A =

N·m/s

weber Wb magnetic flux kg·m²/A·s²V·s = H·A = T·m² = J/A

Name

Symbol Unit ofEquivalent inBase Units

OtherEquivalents

The Prefixes of the SI

yotta [Y]1 000 000 000 000 000 000 000 000

= 1024 (one septillion)

zetta [Z]1 000 000 000 000 000 000 000

= 1021 (one sextillion)

exa [E]1 000 000 000 000 000 000

= 1018 (one quintillion)

peta [P]1 000 000 000 000 000

= 1015 (one quadrillion)

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)

kilo [k]1 000

= 103 (one thousand)

    1 = 100 (one)

The Prefixes of the SI

milli [m]0.001

= 10-3 (one thousandth)

micro []0.000 001

= 10-6 (one millionth)

nano [n]0.000 000 001

= 10-9 (one billionth)

pico [p]0.000 000 000 001

= 10-12 (one trillionth)

femto [f]0.000 000 000 000 001

= 10-15

(one quadrilliont

h)

atto [a]0.000 000 000 000 000 001

= 10-18

(one quintilliont

h)

zepto [z]0.000 000 000 000 000 000 001

= 10-21 (one sextillionth)

yocto [y]0.000 000 000 000 000 000 000 001

= 10-24 (one septillionth)

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.

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)

A. H.B. C.D.E.F.G.

Some Common Conversions

Length and Area:1 foot = 12 inches1 mile = 5,280 feet1 kilometer = 1,000 meters1 mile ≈ 1.6 kilometers1 foot ≈ 0.305 meter1 yard = 3 feet1 mile = 1,760 yards1 meter = 1,000 millimeters1 inch ≈ 2.540 centimeters1 acre = 4,840 square yards1 square yard = 9 square feet1 square foot = 144 square inches

Volume:1 gallon = 4 quarts1 gallon ≈ 231 cubic inches1 liter = 1,000 milliliters1 liter ≈ 1.057 quarts1 gallon ≈ 3.785 liters1 quart = 2 pints1 pint = 16 fluid ounces1 cubic yard = 27 cubic feet1 cubic foot ≈ 7.48 gallons

Weight (on Earth’s surface)1 ton = 2,000 pounds1 kilogram ≈ 2.205 pounds1 pound = 16 ounces1 pound ≈ 0.454 kilogram1 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 symbols2) determine which of two prefixes represents a larger amount3) determine the exponential "distance" between two prefixes4) significant figure rules5) 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

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

DIMENSIONAL ANALYSIS:

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.

MegaKiloHectoDekaBaseDeciCentiMilliMicroNanopico

Cross this linemove decimal by 3for each step.

Cross this linemove decimal by 3for each step.

Move only onedecimal foreach step in this area

Step Method

Going down, decimal moves to the right for each step

Going up, the decimal moves to the left for each step

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

Practice Problems

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. I.B. J.C. K.D. L.E. M.F. N.G. O.H.

For your review try;http://www.aaamath.com/mea.html