MEASUREMENT

Systems of Measurement:
 English System – It has no scientific standard.Another disadvantage is that it can be awkward( Height – 6ft & 11 in). A
third major problem is they lack any systematic relationship between units.
 Systeme International d’ Unites or SI – modified form of the metric system, The key features of the of the SI are
decimalization, a system of prefixes and a standard defined terms of an invariable physical measure. It is simple &
convenient to use since all units are based on multiples of ten

SI Base Units:
Length – meter(m)- length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a
Second
Mass – kilogram(Kg)- mass of the international prototype cylindrical alloy
Time – second (s) – duration of 9,192,631,770 periods of the radiation corresponding to the transition between
2 hyperfine levels of the groundstate in cesium-133 atom
Electrical current – ampere(A)- constant current which if maintained in straight parallel conductors of infinite
length, of negligible circuit cross-section and placed 1 meter apart in vacuum would produce between
those conductors a force equal to 2x10-7newtons per meter of length
Temperature – Kelvin (K) – the fraction 1/273.16 of the thermodynamic temperature of the triple point of water(
triple point- point in a phase diagram where three phases coexist in equilibrium)
Amount of substance- mole(mol) – amount of substance of a system which contains as many elementary
entities as there are atoms in 0.012kg of carbon 12
Luminous intensity – candela(cd) – the luminous intensity in a given direction of a source that emits mono-
chromaticradation of frequency 540x1012herts and that has a radiant intensity in that direction of
1/683 watt per steradian
Prefix Numerical meaning Scientific Notation Symbol
tera 1 000 000 000 000 1012 T
giga 1 000 000 000 109 G
mega 1 000 000 106 M
kilo 1 000 103 K
hecto 100 102 h
deca 10 101 da
deci 0.1 10-1 d
centi 0.01 10-2 c
milli 0.001 10-3 m
micro 0.000001 10-6 u
nano 0.000000001 10-9 n
pico 0.000000000001 10-12 p
femto 0.000000000000001 10-15 f

Measurement Metric SI
Length Meter Meter
Volume Liter Cubic meter
Mass Gram Kilogram
time Seconds Seconds
temperature Degree Celsius Kelvin

Derived Units: Volume, pressure, area, density, energy

Conversion of units:
 Conversion factors- a fraction in which the same quantity is expressed one way in the numerator & another way in the
denominator
 Dimensional analysis/ factor-label method/unit analysis-use of conversion factors in problem solving

Sample Problem:
1) . A unit of beauty , a Helen, thought to have been invented by British mathematician W.A.H. Rushton,
Is based on Helen of Troy(from Christopher Marlowe’s translation of Homer’s Iliad) who is widely
Known as having” the face that launched a thousand ships”. How many ships could be launched by a
Face with 1.00 millihelen of beauty?
2) American writer Cullen Murphy coined a unit of fame, the Warhol, based on artist Andy Warhol’s claim that “ everyone will be
famous for fifteen minutes”, 1 warhol = 15minutes of fame. Entertainer Herbert Khaury (Tiny Tim) was famous , starting 1962
for about 200kilowarhols. How long was that in years?
Mass: measure of the amount of matter in an object or sample
Weight: force exerted by an object or sample due to gravity
Temperature: hotness or coldness of a certain body, measure of the intensity of heat not the quantity
Heat
0C = 0F – 32 0F = 1.8(0C) + 32 K = 0C + 273
1.8
Heat: energy on the move, the energy that flows from a warm object to a cooler one.
Joule (J) – SI derived unit of energy, 1J = Kg-m2/s2
Calorie – more familiar unit, amount of heat required to raise the temperature of 1g of water by 1 oC
-the “calorie “ used for expressing the energy content of foods is actually a kilocalorie (1500 Calories- 1500Kcal)
1 calorie = 4.184 Joules
1000 cal = 1Kcal = 4184J
Volume:
V rectangular shaped solids = lwh V sphere = 4/3 𝜋r3
V cube = S3
V cylinder = = 𝜋𝑟 2
Density:- ratio of the mass of a substance to its volume
Sample problems:
1. A jeweller offers to sell a ring to a woman and tells her that it is made of platinum. Noting that the ring felt a little light, the
woman decides to perform a test to determine the ring’s density. She places the ring on a balance & finds that it has a
mass of 5.84g. She also finds that the ring displaces 0.556cm3 of water. Is the ring made of platinum?Density of platinum
is 1.4g/cm3.
2. The gasoline in an automobile gas tank has a mass of 60.0Kg and a density of 0.752g/cm 3. What is its volume in
L?
3. A titanium cube has a mass of 4.72Kg.What is the measurement of one side of the cube? Density is 4.50g/cm 3
4. Lithium, a soft gray solid with the lowest density of any metal, is akey component of advanced batteries such as
the one in your laptop. A slab of lithium has a mass of 1.49 x 10 3 mg & has sides that are 20.9 mm by 11.1mm by
11.9mm. Find the density of lithium in g/cm3
5. The dimensions of aluminium foil in a box for sale in supermarkets are 66 2/3 yards by 12 inches. The mass of the foil is
0.83kg. If the density is 2.70g/cm3, then what is the thickness of the foil in inches?
Specific gravity or relative density:
Ratio of the density of a substance to the density of a standard or ratio of the mass of an object to the
mass of an equal volume of a standard

Exercises:
1. Many international computer communications are carried by optical fibers in cables laid along the ocean floor . If
one strand of optical fiber weighs 1.19x10-3lbs/m, what is the mass in Kg of a cable made of 6 strands of optical
fiber, each long enough to link New York & Paris ( distance of NY from Paris =8.84 x 103Km)?
2. Convert 4.352 micrograms to megagrams.
3. When 1.00g of gasoline burns, it yields about 10.3Kcal of energy. What is this quantity of energy in kilojoules?(43.1KJ)
4. A graduated cylinder contains 19.9mL of water . When a small piece of galena, an ore of lead is added, it sinks and
the volume increases to 24.5mL. If the density is 7.5g/cm3, What is the mass(Kg) of the ore?
5. A hybrid SUV consumes fuel at a rate of 12.8km/L. How many miles can the car travel on 22.5 galloons of gasoline?
6. A car has a mileage rating of 38 miles per galloon of gasoline. How many miles can the car travel on 76.5L of gasoline?
7. According to the website of the National Aeronautics & space Administration, the average temperature of the
universe is 2.7K. What is this temperature in 0F?
8. A titanium bicycle frame contains the same amount of titatium cube measuring 6.8cm on a side. Use the density of titanium to
calculate the mass in kilograms of titanium in the frame. What would be the mass of a similar frame composed of iron?(density
Ti=4.50g/cm3, Fe= 7.86g/cm3)
9. Wire is often sold in pound spools according to the wire gauge number. That number refers to the diameter of the
wire. How many meters are in a 10.00- lb. spool of 12-gauge aluminum wire? A 12-gauge wire has a diameter of 0.0808
in and aluminum has a density of 2.70g/cm3.
10. Analysis shows the presence of 203ug of cholesterol in a sample of blood. How many grams of cholesterol are present in this
blood sample?
11. The density of mercury is 13.59g/cm3, express the density of Hg in lb/ft3.
12. An iron ore is found to contain 9.24% hematite. A. How many tons of this ore would contain 8.40 tons of hematite? B. How
many Kg of this ore would contain 9.40Kg of hematite?
13. Household ammonia is 5.00% ammonia by mass and has a density of 1.006g/mL. What volume of this solution must a
person purchase to obtain 17.4g ammonia.?

Why are units so important?

On dec 11, 1998 NASA launched the 125 million dollar Mars climate orbiter, which was intended to be the red planet’s first
weather satellite. After a 416 million mile journey the spacecraft was supposed to go into Mar’s orbit on Sept 23,1999. Instead it entered
Mar’s atmosphere about 100 km (6 mi) lower than planned & was destroyed by heat. Mission controllers later determined that the
spacecraft was lost because English measurement units were not converted to metric units in the navigation software.
Engineers at Lockheed Martin Corporation, who built the spacecraft specified its thrust in lbs which is an English unit.Scientist
at NASA’s Jet Propulsion Laboratory on the other hand who were responsible for deployment had assumed that the thrust data they
were given were expressed in Newtons a metric unit. To carry out conversion between pound & newton, we would start with 1 lb=
0.4536Kg & from Newtons second law of motion Force = (mass) ( acceleration)
Because 1N = 1Kg.m/s2. Therefore instead of converting 1 lb of force to 4.45N, the scientist treated it as a force of 1 N. The
considerably smaller engine thrust employed because of the engineers’ failure to convert from English to metric units resulted in a lower
orbit and the ultimate destruction of the spacecraft.