Measurements : The Metric system : ( guide for metric practice)
I) The history of the metric system :
-Metric System: scientists everywhere are using the metric system which is a decimal system
1793- the metric system was devised by the French National Academy of sciences to overcome the profusion of units handed down from medieval times. The united states of America had already adopted a decimal system: Congress had adopted the silver dollar and decimal system of money on August 8, 1786.
1960 The international bureau of weights and measures adopted the international system of units.
1975: The metric conversion Act committed the United States to encourage but not to require the change to metric measurements.
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Table 1 : The fundamental units in the metric system |
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( System International) MKS |
CGS |
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Length |
meter (m) |
centimeter ( cm) |
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Mass |
kilogram (kg) |
gram ( g) |
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time |
second ( s ) |
second (s) |
* Note: Only units named after people are capitalized in the metric system, for example gram is not capitalized but the unit of force Newton is capitalized.
2) A decimal system: units are divided in 10 subunits which correspond to prefixes
| Tera | Giga | Mega | Kilo | Hecto | Deca |
fondamental unit |
deci | centi | milli | micro | nano | pico | ||||||||||||
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
using this chart you find out that 1 Terameter (Tm) would be equal to 1x 1,000,000,000,000,000,000,000,000 picometer (pm) = 1x 1024 pm
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Table 2 : Metric system prefixes |
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| Prefix | Symbol | Factor (decimal or fraction) | Factor ( exponential ) |
| Tera | T | 1,000,000,000,000 | 1012 |
| Giga | G | 1,000,000,000 | 109 |
| Mega | M | 1,000,000 | 106 |
| kilo | k | 1,000 | 103 |
| hecto | h | 100 | 102 |
| deca | dK (or da) | 10 | 101 |
| deci | d | .1 = 1 / 10 | 10-1 |
| centi | c | .01 = 1/100 | 10-2 |
| milli | m | .001 = 1/1,000 | 10-3 |
| micro | µ | .000,001 = 1/ 1,000,000 | 10-6 |
| nano | n | .000,000,001 = 1 / 1,000,000,000 | 10-9 |
| pico | p | .000,000,000,001 = 1 / 1,000,000,000,000 | 10-12 |
4) The international system of Units:
The metric system is based on national standard. The meter is the unit of measure from which all other units where derived.
Length: Distance covered by a line segment connecting two points.
Length units: Are combination of prefixes placed in front of the principal unit of length the meter, each successive unit going toward the left increases by a factor of ten, each unit going toward the right decreases by a factor of ten. For example a meter indicates a measure 100 times larger than a cm and a dkm is 100 times smaller than a cm.
Km, hm, dKm, m, dm, cm, mm, , , :m, , , nm
There are empty space in the scale since no specific units are used for a value for 10 x smaller than a cm for example.
: m= 10 -6 m = micrometer ; nm= 10-9 m= nanometer.
Scale: t, q , , Kg , hg, dkg , g , dg , cg , mg, , , :g, , , ng
The metric unit of mass is the Kilogram, a Kilogram was defined as the quantity of pure water in the form of a cube of 1 dm (.1m =10-1 m) of side at 3.98o C (temperature at which water density of water is greatest)
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Differentiate between mass and weight |
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Mass ( fundamental unit ) |
Weight (derive unit) |
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Definition |
mass represents the quantity of matter in a body |
measure of the force or pull of gravity on a body |
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Instrument of measure |
balance |
spring scale |
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Unit of mass |
(MKS): Kilogram (CGS): gram (gram = 1/1000 Kg) |
Newton (N = kg.m/ s2)
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| on earth | a mass of 1kg | exercises in the field of the earth gravity a force = mass x g (vector field of gravity ) , so a mass of 1kg exercise a force equal to 1kg x 9.8m/s2 = 9.8 Newtons. |
more on mass versus weight :
The principal unit is the liter. The liter is a special name for cubic dm (dm3 ). This is how it was originally defined; it is now defined as the volume occupied by 1 Kg of water at 3.98oC..
Since: 1 m3 = 1 m x 1 m x 1 m <=> 1 m3 = 10 dm x 10 dm x 10 dm = 1000 dm3 = 1000 liters
so 1 dm3 = 1 liter and 1cm3 = 1 ml , 1 :l = 1 mm3
Scale: (Kl) , hl , dKl , l , dl , cl, ml , , , :l
1m3 1dm3 1cm3
Volume and mass relations for water ( at 3.98 C):
1 liter of water has a volume of 1 dm3 = 1000 cm3 and mass of 1Kg
1 ml of water has a volume of 1cm3 and a mass of 1g
Time: interval between two occurrences.
Second: 1/ 86400 of an average day
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Differentiate between Temperature and Heat |
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Heat |
Temperature |
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definition |
Heat: is a form of energy within a system which can be transferred by thermal process. Heat travels from area of higher temperature to area of lower temperature
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A measure of the ability of a system to transfer heat energy or to acquire heat energy from another system. It is the measure of the average translational kinetic energy of the molecules within a system. |
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Heat and temperature |
as a quantity of energy )H = m.C. )T {)H= heat (H) change ()) } m = mass C = specific heat )t = Change in temperature |
)T = )H / m .C |
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Instrument |
Calorimeter |
Thermometer |
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Unit of measure |
calorie = 4.19 joules
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degree Celsius degree Kelvin |
A further example may help to differentiate between heat energy and temperature
The sea and a glass of water can both be raised at the same temperature however they will not require the same amount of heat energy for this to happen.
Later on we will realize that energy on the form of heat may be provided or removed from a system to enhance a physical change ( evaporation / condensation and melting / freezing ). During the change of state such as evaporation and melting although heat energy is provided to the system the temperature does not change. Heat is used to provide the molecules with further kinetic energy by moving them further apart.
Measuring Temperature in the Metric System:
The most usual instrument for measuring temperature is the mercury thermometer, it is based on the nearly linear expansion of liquid mercury and its contraction with changing temperature.
Mercury thermometers are calibrated in the Celsius temperature scale the scale is defined by two fixed points; freezing pt. of water is 0o C and its boiling pt. Is at 100o C ( the unit of temperature is the degree)
Kelvin scale: on the Kelvin scale 0 represents the absolute lowest temperature attainable ( the kelvin scale is not expressed in degrees)
Relation between Celcius and Kelvin temperature 0oC=273 K
Examples: 10oC=273 K+ 10 =283 K
100 K= 100-273 = -173 oC
Measuring Heat in the Metric System:
Unit of heat: the calorie: amount of heat required to raise the temperature of one gram of water of 1 oC., theKilocalorie: amount of heat required to raise the temperature of one Kg of water of 1o C.
An equivalent was established between work and heat which are both forms of energy - unit of work :1 joule = (Force x distance) = N x m = Kg m2 /s2 , 1 calorie = 4.19 joules
Speed: quantity / time Example: meter per second = m/s
Density: mass per unit volume . Link to conversion between unit of density
In chemistry the density of solid and liquids is generally measured in g/cm3 (gram per cubic centimeter) or g/ml (gram per milliliter) remember that a ml is the equivalent of a cubic centimeter .
The example below illustrates the relation existing between the mass and the volume occupied by the element Mercury which is existing as a liquid at room temperature.
What is the mass of 10 cm3 or ml of Mercury ? 270 g of Hg occupy what volume ? 28 ml of Hg would have a mass of how many grams?
What represent the slope of this graph ?
Specific gravity: ratio of the mass of a body to the mass of an equal volume of water at 3.98 oC or other specified temperatures (no unit = ratio)
11) Scientific notation: ( scientific notation explained )
Examples: Distance from Earth to the Moon = 100,000,000 m= 108 m
Diameter of a red blood cell = .00001 m = 10-5 m
Addition and Subtraction: when numbers are expressed in Scientific Notation they can be added or subtracted only if the exponent of ten are equal-
example: 4.0 x 106 +3 x 105 =4.0 x 106 + .3 x 106 = 4.3 x 106
Multiplication: to multiply 2 numbers which are in scientific notation
1. Multiply the numbers preceding the powers of ten
2. Add the exponent of ten to obtain the correct power of ten for the product.
am . an = am+n (4 x 108 )(6 x 106 ) = 24 x 108+6 = 24 x 1014
Division:
to divide numbers expressed in scientific notation
1. Divide the numbers preceding the powers of ten
2. Subtract the exponent of ten in the denominator from the exponent of the power of ten in the numerator
am / an = am-n 5(10)6 / 2(10)7 = 2.5(10)6-7 = 2.5 . 10-1
12) the factorial method to convert between units:
example 1: if you want to convert 12 kg in milligrams the idea is to divide by the unit you want to get read off (kg ) and multiply by the equivalent of the unit you want to replace ( 1,000,000mg is the equivalent of 1kg ) .
12kg x 1,000,000mg
= 12,000,000mg
1kg
example 2: if you want to convert the value of 5cm into meters the idea is to divide by the equivalent of unit you want to get read off (cm) and multiply by the unit you want to replace it by the meter . Since the equivalent of 1 meter in cm is 100cm you will divide by 100cm and multiply by one meter.
5cm x 1m
_____________ = .05m
100 cm
13)
Conversions between the Metric System and the English System :
| Volume SI unit: cubic meter (m3) 1 liter = 10-3m3 = 1 dm3 = 1.0567 quarts 1 gallon = 4 quarts = 8 pints = 3.7854 liters 1 quart = 32 fluid ounces = 0.94633 liter |
Energy SI unit: joule (J) 1 joule = 1 kg · m2/s2 = 0.23901 calorie = 9.4781 x 10-4 btu (British thermal unit) 1 calorie = 4.184 joules = 3.965 x 10-3 btu 1 btu = 1055.06 joules = 252.2 calories |
| Temperature SI unit: kelvin (K) 0 K = -273.15°C = -459.67°F K = °C + 273.15 °C = (5/9)(number of °F-32) °F = (9/5)(number of °C)+32 |
Pressure SI unit: pascal (Pa) 1 pascal = 1 N/m2 =1 kg/m · s2 / m2 1 atmosphere = 101.325 kilopascals = 760 torr (mmHg) = 14.70 pounds per square inch 1 bar = 105 pascals |
Temperature : relationship between Celsius scale and Fahrenheit scale :
divide 5 by 9 , what is the decimal value of the ratio, multiply 5/9 by -32 what is the number you are finding relate your findings to the equation of the graph ( Y = .5556x -17.778 ) .
14) Accuracy and Precision : (see links and activities on top table)
15) Uncertainty in Measurement :(see links and activities on top[ table)
16) Significant digits: (see links and activities on top table)
a) Density :
An object has a rectangular shape: width = 5cm, length is the 10cm, height= 4cm and its mass is 20g.
Find the density of the object and compare it ti the density of the water
Find the density of a sphere which has a diameter of 12 mm and a mass =4.0g
Find the density of a cylinder which has the radius of 20mm, a height of 40mm and a mass of 54.28g.
An object has a cubic shape and a density of .9g /cm3 And a mass of 24.3g what is the length of the side of the cube?
b) Conversions:
20 cm= mm 8.5Kg = g
82 l = dl 2 dm3 = ml
7.5 l = ml 8.62 ml= l
200 K= oC 5.02ml= l
200 oC= K 32 cl = ml
What is the weight in grams of a block of silver measuring 2.5cm, 8cm and 4cm given that the density of silver is 10.5 g/cm3 ?
A graduated cylinder contained 20.0 ml of water. When 100g of shot were added to the cylinder the water level read 32.6 ml what is the density of brass?
How many milliliters are there in 500 g of mercury given that the density of mercury is 13.6 g / ml?
Express as a whole #: 6.2 x 102 = 3.5 x 105 = 6.2 x 101 = 4.5 x 103 =
Express in scientific notation: 245.82= .002= 14.25= .023=
Perform the operations: 3.21 x 102 + 1.5 x 104 = 6.2 x 103 +4.5 x 102 = (5 x 102 )(3 x 101 )= (6.2 x 103 ) (2 x 104) =
The bond length between the hydrogen and the atom of chlorine is .127 nanometer in hydrochloric acid: express this length in meter and in cm,
Same question between oxygen and carbon in carbon monoxide the bond length being = .12 nanometers