Tuesday, March 26, 2013

Chemistry lecture 17



Metric - US/Imperial measurement units

 The Imperial System (which uses yards, feet, inches, etc to measure length) was developed over hundreds of years in the UK, then the French developed the Metric System (metres) in 1670, which soon spread through Europe, even to England itself in 1963. But the USA and a few other countries still prefer feet and inches.

°F to °C
Deduct 32, then multiply by 5, then divide by 9
°C to °F
Multiply by 9, then divide by 5, then add 32

Length

Metric

US or Imperial
1 millimetre [mm]

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0.03937 in
1 centimetre [cm]
10 mm
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0.3937 in
1 metre [m]
100 cm
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1.0936 yd
1 kilometre [km]
1000 m
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0.6214 mile

US or Imperial

Metric
1 inch [in]

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2.54 cm
1 foot [ft]
12 in
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0.3048 m
1 yard [yd]
3 ft
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0.9144 m
1 mile
5280ft
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1.6093 km
1 int nautical mile
2025.4 yd
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1.853 km

Area

Metric

US or Imperial
1 sq cm [cm2]
100 mm2
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0.1550 in2
1 sq m [m2]
10,000 cm2
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1.1960 yd2
1 hectare [ha]
10,000 m2
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2.4711 acres
1 sq km [km2]
100 ha
http://www.mathsisfun.com/images/arrow.gif
0.3861 mile2

US or Imperial

Metric
1 sq inch [in2]

http://www.mathsisfun.com/images/arrow.gif
6.4516 cm2
1 sq foot [ft2]
144 in2
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0.0929 m2
1 sq yd [yd2]
9 ft2
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0.8361 m2
1 acre
4840 yd2
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4046.9 m2
1 sq mile [mile2]
640 acres
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2.59 km2

Conversion of Area

To convert area, simply remember that area is length by width:
Area = Length *Width

Volume/Capacity

Metric

US Measure
Imperial
1 cu cm [cm3]

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0.0610 in3
1 cu decimetre [dm3]
1,000 cm3
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0.0353 ft3
1 cu metre [m3]
1,000 dm3
http://www.mathsisfun.com/images/arrow.gif
1.3080 yd3
1 litre [l]
1 dm3
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2.113 fluid pt
1.7598 pt
 
US Measure
Imperial

Metric
1 cu inch [in3]
http://www.mathsisfun.com/images/arrow.gif
16.387 cm3
1 cu foot [ft3]
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0.02832 m3
1 fluid ounce
1.0408 UK fl oz
to
29.574 ml
1 pint (16 fl oz)
0.8327 UK pt
to
0.4732 liters
1 gallon (231 in3)
0.8327 UK gal
to
3.7854 liters

                                                               Conversion of Volume

Volume is Height by Width by Length

http://www.mathsisfun.com/geometry/images/cuboid.gif

To convert Volume, remember that volume is height by width by length:
Volume = Height   *Width *Length
 1quarts= 0.946liter  1quart=2pints  1quart=32fluid ounces
Calculate the mass of the liquid   m=d*V

Mass

1ton=2000pounds   1amu=1.661*10-24g
Metric

US or Imperial
1 milligram [mg]

http://www.mathsisfun.com/images/arrow.gif
0.0154 grain
1 gram [g]
1,000 mg
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0.0353 oz
1 kilogram [kg]
1,000 g
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2.2046 lb
1 tonne [t]
1,000 kg
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1.1023 short ton
1 tonne [t]
1,000 kg
to
0.9842 long ton




 
US or Imperial

Metric
1 ounce [oz]
437.5 grain
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28.35 g
1 pound [lb]
16 oz
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0.4536 kg
1 stone
14 lb
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6.3503 kg
1 hundredweight [cwt]
112 lb
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50.802 kg
1 short ton (US)

to
0.9072 t
1 long ton (UK)

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1.0160 t
Some examples will help:

Example 1

What is 2,000 yards in Metric?
1. In the chart it shows that 1 yd = 0.9144 m (metres)
2. Multiply 2,000 x 0.9144 = 1,829 m
3. 1,829 m would be better expressed as 1.829 km (kilometres)

Example 2

What is 50 cubic foot in Metric?
1.      In the chart it shows that 1 cu foot = 0.0283 m3 (cubic metres)
2. Multiply 50 x 0.0283 = 1.415 m3
3. Looks Good !
Density
                     m                      301g
D= -------------- =   ---------------- = 19.3g/cm3

                 V                  15.6cm3           

 

Metric Numbers

In the Metric System there are standard ways of talking about big and small numbers:
  • "kilo" for a thousand,
  • "mega" for a million,

 

"kilo", "mega", "milli" etc are called "prefixes":
Prefix: a word part that can be added to the beginning of another word to create a new word
So, using the prefix "milli" in front of "liter" creates a new word "millilter".
Scientists and Engineers (who often use very big or very small numbers) like to write numbers this way.

Example: The Mass of the Sun

The Sun has a Mass of 1.988 * 1030 kg.
It would be too hard for scientists to write 1,988,000,000,000,000,000,000,000,000,000 kg
(And very easy to make a mistake counting the zeros!)

Here we list the prefix for commonly used big and small numbers:

Common Big and Small Numbers

Name
The Number
Prefix
Symbol
trillion
1,000,000,000,000
tera
T
billion
1,000,000,000
giga
G
million
1,000,000
mega
10 6M
thousand
1,000
kilo
10 3k
hundred
100
hecto
h
ten
10
deka
10 1da
unit
1


tenth
0.1
deci
10 -1d
hundredth
0.01
centi
10 -2c
thousandth
0.001
milli
10 -3m
millionth
0.000 001
micro
10 -6µ
billionth
0.000 000 001
nano
10 -9n
trillionth
0.000 000 000 001
pico
p

length continuum

 

Place Value and Decimal

Our Number System is based on ten.
Using only ten symbols (called Digits) we can write any number.

The Ten Digits

The Digits we use today are called "Hindu-Arabic Numerals" and look like these:
0   1   2   3   4   5   6   7   8   9
So we know that we have 1 Ten and 2 Ones, which makes 12.
This could also be written as 1 * 10 + 2 *1.
Example: "35" means 3 Tens and 5 Units, which is also 3 *10 + 5 * 1
http://www.mathsisfun.com/images/decimals.gif


Definition of Decimal

http://www.mathsisfun.com/images/style/blue-speech.gifThe word "Decimal" really means "based on 10" (From Latin decima: a tenth part).
We sometimes say "decimal" when we mean anything to do with our numbering system, but a "Decimal Number" usually means there is a Decimal Point.

Fractions

A fraction is a part of a whole

Slice a pizza, and you will have fractions:

http://www.mathsisfun.com/images/fractions/pie-1-2.jpg
http://www.mathsisfun.com/images/fractions/pie-1-4.jpg
http://www.mathsisfun.com/images/fractions/pie-3-8.jpg
1/2
1/4
3/8
(One-Half)
(One-Quarter)
(Three-Eighths)



Numerator
_____________



Denominator











1.


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