Units and measurements

Measurement

You are making a measurement when you

Check you weight
Read your watch
Take your temperature
Find your height

What kinds of measurements did you make

today?
 Some Tools for Measurement
When we measure, we use a
measuring tool to compare some
dimension of an object to a
standard.

In every measurement there is

Number (quantity)
followed by a

 Unit from measuring device

 Stating a Measurement

A physical quantity is one that can be measured and

consists of a magnitude and unit.
Measurement : It is the comparison of an unknown
quantity with a known standard quantity (constant
quantity) or unit
Unit : The standard quantity (constant quantity) used
for comparison is called unit.
The standard unit should be easily reproducible,
internationally accepted
 Physical quantities and their units
Physical quantities may be broadly
divided into fundamental and Base quantity is like the
derived quantities brick – the basic building
block of a house
 Fundamental quantity :
Fundamental quantities are
independent quantities from Derived quantity is like
which other quantities can be
obtained, e.g. length, mass and the house that was
time build up from a collection
of bricks (basic quantity)
 Derived quantity : Derived
quantity is one which is obtained
with the help of one or more
fundamental quantities, e.g. area,
volume, density and speed
 Units

 A fundamental unit is the unit of a fundamental

quantity
 Derived units are obtained from the
fundamental units by multiplication or division
 Systems of Units

 Earlier three different units systems were used in

different countries. These were CGS, FPS and MKS
systems.
 Now-a-days internationally SI system of units is
followed.
 In SI unit system, seven quantities are taken as the base
quantities.
 Supplementary units – radian (rad) for angle and
steradian (sr) for solid angle
 (i) CGS System: Centimetre, Gram and Second are used
to express length, mass and time respectively
(ii) FPS System: Foot, pound and second are used to
express length, mass and time respectively.
(iii) MKS System: Length is expressed in metre, mass is
expressed in kilogram and time is expressed in second.
Metre, kilogram and second are used to express length,
mass and time respectively
 (iv) SI system: Length, mass, time, electric current,
thermodynamic temperature, Amount of substance and
luminous intensity are expressed in metre, kilogram,
second, ampere, kelvin, mole and candela respectively.
 Basic Units

Base Quantities Name of Unit Symbol of Unit

length metre m

mass kilogram kg

time second s

electric current ampere A

temperature kelvin K

amount of substance mole mol

luminous intensity candela cd

Derived Units

• Example of derived quantity: area

Defining equation: area = length × breadth
In terms of units: Units of area = m × m = m2
Defining equation: volume = length × width × height
In terms of units: Units of volume = m × m × m = m2
Defining equation: density = mass ÷ volume
In terms of units: Units of density = kg / m3 = kg m−3
Derived SI Units (examples)
Quantity unit Symbol

Volume cubic meter m3

Density kilograms per cubic kg/m3

meter
Speed meter per second m/s

Newton kg m/ s2 N

Energy Joule (kg m2/s2) J

Pressure Pascal (kg/(ms2) Pa

 Rules to be observed

The following rules should be observed while using S.I.

system of units
 The symbols should not contain a full stop. For example, we
should write kg (not kg.)
 The symbol should remain the same in plural form also. For
example, mass should be written as 20 kg (not 20 kgs)
 If a unit is named after a person, the symbol for the unit
should start with a capital letter. Thus, the symbol for the unit
of force , newton is N
 When the full name of the unit is written the first letter should
not be capital. For example, we should write newton not
Newton
 Symbols with other units should not start with a capital letter.
For example, we should write kg for kilogram
 No punctuation marks or full stops should be used at the end
of the symbol
 Space is to be left between the numerical and symbol e.g 20 s
and not as 20s
The symbol has a capital letter when the unit is named after a
person

Derived quantities units

Name Symbol
Force newton N
Pressure pascal Pa
Energy , work joule J
Power watt W
Frequency hertz Hz
Electric charge coulomb C
Electric resistance ohm Ω
Electromotive force volt V
Prefixes
Prefixes simplify the writing of very large or very
small quantities

Prefix Abbreviation Power

nano n 10−9
micro  10−6
milli m 10−3  1 ft = 12 in.

centi c 10−2  1 yd = 3 ft
deci d 10−1  1 mi = 5,280ft =
kilo k 103 1,760 yd
mega M 106
giga G 109
 Advantages of the SI system

The advantages of the SI system are,

 SI system is based on the precise and definite standards.
 This system makes use of only one unit for one physical quantity,
which means a rational system of units
• In this system, all the derived units can be easily obtained from
basic and supplementary units, which means it is a coherent
system of units.
• It is a metric system which means that multiples and submultiples
can be expressed as powers of 10
• Without the use of conversion factors, the SI units can be derived
from one another.
 Metre- definition

 In 1791, the Paris Academy of Sciences defined metre as one

millionth part of distance from the pole to the equator
 This distance is marked between two parallel lines drawn on a
platinum- iridium bar
 This is kept at a constant temperature in the International Bureau
of weights and measures at Sevres near Paris
 One metre is defined as 1,650,763.73 times the wavelength of
specified orange –red spectral line in emission spectrum of
Krypton -86
Distance and Length
 Distance and Length
▪ measurement -
— a quantity and a unit
▪ distance -
— is a length
— the amount of space between
two points
• Correct way to read the scale on a ruler
• Position eye perpendicularly at the mark on the scale to
avoids parallax errors
• Another reason for error: object not align or arranged
parallel to the scale
 Important conversions

 1 Light year = 9.46 x 10 15 m

 1 Astronomical unit = 1.496 x 10 11 m
 1 micron = 10 -6 m
 1 Angstrom = 10 -10 m
 1 fermi = 10 -15 m
 Mass
The mass of an object is a measure of
the quantity of material it contains.
- in the metric system, the mass unit is
the gram (g).
- in the SI system, the mass unit is the
kilogram (kg).
- Mass is not the same thing as weight

weight
is the force of the Earth’s gravity
pulling down.
Gravity acts on an object’s mass
 Kilogram -definition

 The unit of mass is kilogram

 One kilogram is the mass of the platinum – iridium
cylinder of diameter equal to its height kept at the
international bureau of weights and measures near
Paris
 Practical units : Gram = 10 -3 kg, milligram (mg) = 10 -6
kg, Quintal (q) = 10 -2 kg, Ton = 1000 kg

 1 pounds = 16 ounces
 1 Ton = 2,000 pounds
 Second – definition

 The unit of time is second

 One second is defined as the duration of 9192 631 770
periods of the radiation corresponding to the transition
between two specified energy levels of cesium -133
atom
 Basic units : microseconds (μs) = 10 -6 s; milliseconds
(ms) = 10 -3 s; minute = 60s; hour = 3600s
Mass Weight

•Weight is the measure of the amount of

•Mass is simply the measure of the amount
force acting on a mass due to acceleration
of matter in a body.
due to gravity.

•The SI unit of mass is kilogram (kg). •The SI unit of weight is newton (N).
•Weight is the measure of the gravitational
•Mass is always constant for a body and force acting on a body.
there are several formulas to calculate mass. •Weight can be calculated from the
•One way to calculate mass is: following formula:
Mass = volume × density Weight = mass × acceleration due to
gravity

•Weight is a derived quantity.

•Mass is a base quantity.
•Weight has both magnitude and direction
•Mass only has magnitude and so, it is a
(towards the centre of gravity) and so, it is a
scalar quantity.
vector quantity.

•Mass can be easily measured using any

•Weight can be measured by a spring
ordinary balance like beam balance, lever
balance or by using its formula.
balance, pan balance, etc.
 Time

 Two ways to think about time:

 What time is it?
 3 P.M.
 How much time has passed?
 3 hr: 44 min: 25 sec.
 A quantity of time is often called a time interval.
 Converting Mixed Units

1 minute = 60 sec , 1 hour = 60 min

Do the conversion:
1 hour = 3,600 sec
26 minutes = 26 × 60 = 1,560 sec
Add all the seconds:
t = 3,600 + 1,560 + 31.25 = 5,191.25 sec
Time Units
 Convert 55.00 km/h to m/s

55.00 km x 1000 m x 1 h___ = 15.28m/s

h 1 km 3600 s
Volume Unit – the Liter (L)
1 gallon = 4 quarts
1 liter (L) = 1.06 quart
1 quart = 946 mL
1 L = 10 deciliters (dL)
= 100 centilliters (cL)
= 1000 milliliters (mL)

Volume is the amount of space occupied by a

substance. The metric system uses the liter (L)
as the standard volume unit.
- the milliliter (mL) is commonly used for
measuring smaller volumes of fluids in
hospitals and laboratories.
 A Cubic Volume
A cube measuring 10 cm
on each side has a volume
of 1000 cm3, or 1 L. A
cube measuring 1 cm on
each side has a volume of
1 cm3 (cc) or 1 ml.

A plastic
intravenous fluid
container contains
1000 ml.
Density is a measure of mass per unit of volume. The
larger the mass of a substance relative to its volume, the Density
denser (and heavier) it is. The density of a subtance can
be calculated using the following formula:
Mass of Substance
Density =
Volume of Substance
 DENSITY

 Combination of base units.

 Volume - length  length  length
1 cm3 = 1 mL 1 dm3 = 1 L
 Density - mass per unit volume (g/cm3)

M M
D=
V D V
 An object has a volume of 825 cm3 and a density of 13.6
g/cm3. Find its mass.

GIVEN: WORK:
V = 825 cm3 M = DV
D = 13.6 g/cm3
M = (13.6 g/cm3)(825cm3)
M=?
M M = 11,220 g

D V
1) A liquid has a density of 0.87 g/mL. What volume is
occupied by 25 g of the liquid?

GIVEN: WORK:
D = 0.87 g/mL V=M
V=? D
M = 25 g V= 25 g
M 0.87 g/mL
D V V = 28.7 mL
2) You have a sample with a mass of 620 g & a volume of 753
cm3. Find density.

GIVEN: WORK:
M = 620 g D=M
V = 753 cm3 V
D=? D= 620 g
M 753 cm3
D V D = 0.82 g/cm3
Lab Test Values Are Often Reported As per dL
Some Typical Clinical Lab Test Values
Substance in Blood Typical Range

Albumin 3.5 ─ 5.0 g/dL

Ammonia 20 ─ 150 μg/dL
Calcium 8.5 ─ 10.5 mg/dL

Cholesterol 105 ─ 250 mg/dL

Iron (male) 80 ─ 160 μg/dL
Protein (total) 6.0 ─ 8.0 g/dL
 Dimensions

 The powers of the fundamental units in terms of which a physical

quantity can be represented are known as dimensions
 The fundamental units of length, mass and time may be denoted
by letter L,M and T
 Any other physical quantity can be expressed interms of these
letters
 E.g speed = distance/time = L/T = LT-1
 Force = mass x acceleration = MLT-2
 Limits of Measurement - Accuracy and Precision

 Accuracy - a measure of how close a measurement is

to the true value of the quantity being measured.
 is the quality of being exact and free from error.
 Example: Accuracy
 Who is more accurate when measuring a book that has a true
length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
 Precision – a measure of how close a series of
measurements are to one another. A measure of
how exact a measurement is.
 Example: Precision
Who is more precise when measuring the same 17.0cm book?

Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
 Example: Evaluate whether the following are precise, accurate
or both.

Accurate Not Accurate Accurate

Not Precise Precise Precise
 Accurate Measurement

• No measurement is perfectly accurate

• Some error is inevitable even with high precision instruments
• Two main types of errors
– Random errors
– Systematic errors
 Errors

 Random Errors :
 Random errors occur in all measurements.
 small changes in readings while taking measurements are called
random errors
 It is called random errors because they are unpredictable
 It may be due to (i) small changes in the conditions of
measurement and (ii) the incorrect judgement of the observer in
making a measurement
 These errors can be minimized by taking arithmetic mean of a
large number of measurements of the same quantity
 Arithmetic result will be very close to the correct result
 Systematic errors

• Systematic errors are not random but constant

• Cause an experimenter to consistently underestimate or
overestimate a reading
• They are due to the equipment being used – e.g. a ruler with zero
error
• may be due to environmental factors – e.g. weather conditions on
a particular day
• Cannot be reduced by averaging, but they can be eliminated if the
sources of the errors are known
 Instrumental errors : if any instrument used for measurement is
defective, it may lead to instrumental errors
 Since the reason for these errors are known, they are also called as
systemic errors
 To eliminate these errors the measurements are corrected
accordingly
 Percent Error

The percentage error, also known as percent error, is

a measure of how inaccurate a measurement is,
standardized to how large the measurement is.

 PE = (|true value – experimental value| / true

value) x 100%.
 PE = (|theoretical value – experimental value| /
theoretical value) x 100%.
 Applications of units and measurement in
Hospital environment
 To measure height, weight, chest and head circumferences and
abdominal width of the patient
 To measure urine output, oral intake of the patient
 To administer the correct dose of drugs to the patient by adopting
the standard units and measurements
 To check the temperature to monitor the condition of the patient
 To measure blood pressure every time as per the routine to
identify the changes in blood pressure
 Application of forces in traction
 Motion, gravity and centre Molecular physics density
of gravity
 Injuries from moving objects,  Adhesive tape, meniscus of
falling bodies fluids
 Centrifuge  Mercury in thermometers
 Postoperative position  Blood clotting, colloidal drugs
 tension  Antiseptics and surface
 Viscosity of blood
 Elasticity of the blood vessels
 Specific gravity of urine
 Circulation of blood
 Body mechanics
 Crutch walking
Work energy mechanics Heat energy
 Potential and kinetic  Thermometry
energy in circulation of  Body temperature
blood  Application of heat and
 Lifting and turning cold
patients  Steam inhalation
 Massage
 Fever therapy
 Lubricants
 Use of water bath,
blankets
Pressure Wave motion Electricity
 Blood pressure  Microscopy, vision  Removal of foreign
 Air and water  Visual fields, bodies
mattresses refraction  Radium therapy,
 Pulse and respirator  Optics, radioactivity
 Suction apparatus ophthalmoscope  High energy
 Autoclave  Ultraviolet radiation radiation
 Artificial respiration  X- ray therapy  Operating room
 Deafness, hearing precaution
aids  Electric shock
 Audiometer therapy
 ECG, EEG,EMG
 Conclusion

 Clinical procedure involve accuracy, when one person measures a

quantity of fluid, weight, or a temperature, another person
measuring the same quantity should obtain the same results
 Without accuracy there would be little error in reporting
observations and findings
 To achieve this uniformity we should have the system of
measurement
Thank you