Lesson 1.1 - The effects of instruments on measurements Lesson 1.2 - Uncertainties and deviations in measurements Lesson 1.3 - Errors

1. Physical Quantities
and Measurements
The Effects of Instruments on Measurement

2. The Measuring Process
•Measurement is a process of comparing
something with a standard.

3. History of Measurements
• Ancient civilization uses heavenly bodies, body parts, animals or seeds for
measuring.
• 2 systems of units:
• Metric System - mks system (meter, kilogram, second)
- cgs system (centimeters, grams, second)
• English System - fps system (foot, pound, second)
• International System of Units (SI) – French Le Système International d’Unités
• The modern form of the metric system.

4. • It is the system of units that the General Conference on Weights and Measures
(the governing body) has agreed upon.
• It is imposed on almost all parts of the world.
• Physical Quantity – it is a property that can be measured. It can also refer to the
measurement itself.
• Base Units – These are 7 selected units corresponding to 7 base physical
quantities
• Derived Units – These are 22 units derived from the base units. It is formed
by powers, products, or quotients of the base units and are potentially
unlimited in number.
• The current way of defining the SI system is a result of a decades-long move
towards increasingly abstract and idealized formulation in which
the realizations of the units are separated conceptually from the definitions. A
consequence is that as science and technologies develop, new and superior
realizations may be introduced without the need to redefine the unit.

5. Unit
name
Unit
symbol
Dimension
symbol
Quantity
name
Definition
second
s T time
Prior: (1675) 1/86400 of a day of 24 hours of 60 minutes of 60 seconds.
Interim (1956): 1/31556925.9747 of the tropical year for 1900 January 0 at 12
hours ephemeris time.
Current (1967): The duration of 9192631770 periods of the radiation
corresponding to the transition between the two hyperfine levels of the ground
state of the caesium-133 atom
metre m L length
Prior (1793): 1/10000000 of the meridian through Paris between the North Pole
and the Equator.
Interim (1889): The Prototype of the metre chosen by the CIPM, at the
temperature of melting ice, represents the metric unit of length.
Interim (1960): 1650763.73 wavelengths in vacuum of the radiation corresponding
to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.
Current (1983): The distance travelled by light in vacuum in 1/299792458 second.
Base Quantities and Units in SI

6. ampere A I electric current
Prior (1881): A tenth of the electromagnetic CGS unit of current. The [CGS]
electromagnetic unit of current is that current, flowing in an arc 1 cm long of a
circle 1 cm in radius that creates a field of one oersted at the centre
Interim (1946): The constant current which, if maintained in two straight parallel
conductors of infinite length, of negligible circular cross-section, and placed 1 m
apart in vacuum, would produce between these conductors a force equal
to 2×10−7 newtons per metre of length.
Current (2019): The flow of 1/1.602176634×10−19 times the elementary
charge e per second.
kelvin K Θ
thermodynamic
temperature
Prior (1743): The centigrade scale is obtained by assigning 0 °C to the freezing point
of water and 100 °C to the boiling point of water.
Interim (1954): The triple point of water (0.01 °C) defined to be exactly 273.16 K
Previous (1967): 1/273.16 of the thermodynamic temperature of the triple point of
water
Current (2019): The kelvin is defined by setting the fixed numerical value of
the Boltzmann constant k to 1.380649×10−23 J⋅K−1, (J = kg⋅m2⋅s−2), given the
definition of the kilogram, the metre, and the second.
kilogram
kg M mass
Prior (1793): The grave was defined as being the mass (then called weight) of one
litre of pure water at its freezing point.
Interim (1889): The mass of a small squat cylinder of ≈47 cubic centimetres of
platinum-iridium alloy kept in the Pavillon de Breteuil, France. Also, in practice, any
of numerous official replicas of it.
Current (2019): The kilogram is defined by setting the Planck constant h exactly
to 6.62607015×10−34 J⋅s (J = kg⋅m2⋅s−2), given the definitions of the metre and the
second Then the formula would be kg = h/6.62607015×10−34⋅m2⋅s−1

7. mole mol N
amount of
substance
Prior (1900): A stoichiometric quantity which is the equivalent mass in grams
of Avogadro's number of molecules of a substance.ICAW
Interim (1967): The amount of substance of a system which contains as many
elementary entities as there are atoms in 0.012 kilogram of carbon-12.
Current (2019): The amount of substance of exactly 6.02214076×1023 elementary
entities. This number is the fixed numerical value of the Avogadro constant, NA,
when expressed in the unit mol−1 and is called the Avogadro number.
candela cd J
luminous
intensity
Prior (1946): The value of the new candle (early name for the candela) is such that
the brightness of the full radiator at the temperature of solidification of platinum is
60 new candles per square centimetre.
Current (1979): The luminous intensity, in a given direction, of a source that emits
monochromatic radiation of frequency 5.4×1014 hertz and that has a radiant
intensity in that direction of 1/683 watt per steradian.
Note: both old and new definitions are approximately the luminous intensity of
a spermaceti candle burning modestly bright, in the late 19th century called a
"candlepower" or a "candle".

8. Derived Quantities and Units in SI
Name Symbol Quantity In SI base units In other SI units
radian rad plane angle m/m 1
steradian sr solid angle m2/m2 1
hertz Hz frequency s−1
newton N force, weight kg⋅m⋅s−2
pascal Pa pressure, stress kg⋅m−1⋅s−2 N/m2
joule J energy, work, heat kg⋅m2⋅s−2 N⋅m = Pa⋅m3
watt W power, radiant flux kg⋅m2⋅s−3 J/s

9. coulomb C electric charge s⋅A
volt V
electrical potential
difference (voltage), EMF
kg⋅m2⋅s−3⋅A−1 W/A = J/C
farad F Capacitance kg−1⋅m−2⋅s4⋅A2 C/V
ohm Ω
resistance, impedance,
reactance
kg⋅m2⋅s−3⋅A−2 V/A
siemens S electrical conductance kg−1⋅m−2⋅s3⋅A2 Ω−1
weber Wb magnetic flux kg⋅m2⋅s−2⋅A−1 V⋅s
tesla T magnetic flux density kg⋅s−2⋅A−1 Wb/m2
henry H inductance kg⋅m2⋅s−2⋅A−2 Wb/A
degree
Celsius
°C
temperature relative to 273.15
K
K

10. lumen lm luminous flux cd⋅sr cd⋅sr
lux lx illuminance m−2⋅cd lm/m2
becquerel Bq radioactivity (decays per unit time) s−1
gray Gy absorbed dose (of ionizing radiation) m2⋅s−2 J/kg
sievert Sv equivalent dose (of ionizing radiation) m2⋅s−2 J/kg
katal kat catalytic activity mol⋅s−1

11. Scientific Notation
• It is a convenient and widely used method of expressing large and small numbers.
• Any quantity may be expressed in the form of
N x 10 n
Where: N is any number between 1 to 10
n is the appropriate power of 10. It may be positive
or negative
• Give the scientific notation of the following:
a. speed of light is 300000000 m/s
b. mass of a hair strand is 0.00000062 kg

12. SI Prefix Base 10 Decimal
English word
Name Symbol Short scale Long scale
Yotta Y 1024 1000000000000000000000000 septillion quadrillion
Zetta Z 1021 1000000000000000000000 sextillion trilliard
Exa E 1018 1000000000000000000 quintillion trillion
Peta P 1015 1000000000000000 quadrillion billiard
Tera T 1012 1000000000000 trillion billion
Giga G 109 1000000000 billion milliard
Mega M 106 1000000 million
Kilo k 103 1000 thousand
Hecto h 102 100 hundred
Deca da 101 10 ten
100 1 one

13. Deci D 10−1 0.1 tenth
Centi c 10−2 0.01 hundredth
Milli m 10−3 0.001 thousandth
Micro μ 10−6 0.000001 millionth
Nano n 10−9 0.000000001 billionth milliardth
Pico p 10−12 0.000000000001 trillionth billionth
Femto f 10−15 0.000000000000001 quadrillionth billiardth
Atto a 10−18 0.000000000000000001 quintillionth trillionth
Zepto z 10−21 0.000000000000000000001 sextillionth trilliardth
Yocto y 10−24 0.000000000000000000000001 septillionth quadrillionth

14. Rules and Conventions in writing SI units and their symbols
1. The units named after scientists are not written with a capital initial letter. (newton, henry, watt)
2. The symbols of the units named after scientist should be written by a capital letter. (N for newton, H for
henry, W for watt)
3. Small letters are used as symbols for units not derived from a proper name. (m for metre, kg for kilogram)
4. No full stop or other punctuation marks should be used within or at the end of symbols. (50 m and not as 50
m.)
5. The symbols of the units do not take plural form. (10 kg not as 10 kgs)
6. When temperature is expressed in kelvin, the degree sign is omitted. (273 K not as 273 oK)
7. Use of solidus is recommended only for indicating a division of one letter unit symbol by another unit
symbol. Not more than one solidus is used. (m s-1 or m / s, J / K mol or J K–1 mol–1 but not J / K /
mol.)
8. Some space is always to be left between the number and the symbol of the unit and also between the symbols
for compound units such as force, momentum, etc. (23 m not as 23m; kg m s–2 and not as kgms-2)
9. Only accepted symbols should be used. (ampere is represented as A and not as amp. or am ; second is
represented as s and not as sec)
10. Numerical value of any physical quantity should be expressed in scientific notation. (density of mercury is
1.36 × 104 kg m-3 and not as 13600 kg m-3.)

15. Express the following terms of base SI units:
• The ampere, the SI unit of current = charge / time interval
• The joule, the SI unit of work = force x displacement
• The watt, the SI unit of power = work
time interval

16. Conversion of Measurements to SI Units
• To convert measurements to SI units, use common conversions (for
example, 1 hour = 60 minutes = 3600 seconds), or definitions of unit
prefixes (for example, 1 mm = 10-3 m).
• The trick is to write the conversion as a ratio and multiply it to the
measurement.
For samples refer from Exploring Life Through Science General Physics 1 p. 9

17. Convert 6.5 km to meter?
• Given: ?
• Find: ?
• Formula: ?
• Solutions: ?
• Answer: ?

18. Convert 2.7 square centimeters to m2
• Given: ?
• Find: ?
• Formula: ?
• Solutions: ?
• Answer: ?

19. Convert 30 kilometres per hour to m/s
• Given: ?
• Find: ?
• Formula: ?
• Solutions: ?
• Answer: ?

20. A piece of metal measures 2 mm x 5 cm x 1.5 m and its
mass is 1.35 kg. Calculate:
a. the volume of the metal piece in m3
b. the density of the material in kg/m3
Given: ? Solutions?
Find: ? Answer?
Formula: ?

21. A Liter is equal to 1000 cm3. How much cola is in a 1.5 L
bottle?
a. in cm3
b. in m3
Given: ? Solutions?
Find: ? Answer?
Formula: ?

22. Convert a density of 2.79 g/cm3 to kg/m3
• Given: ?
• Find: ?
• Formula: ?
• Solutions: ?
• Answer: ?

23. One light-year (ly) is the distance travelled by light in a year.
Convert one light-year to meters using 3 x 108 m/s for the
speed of light.
(Hint: d = vt)
Given: ? Solutions?
Find: ? Answer?
Formula: ?

24. Physical Quantities
and Measurements
Uncertainties and Deviations

25. Measuring Instruments
• Accuracy is how close a measurement is to the expected or correct value
(true value) of a physical quantity. It is synonymous to validity.
• Precision of a measurement system refers to how close or consistent the
agreement is between repeated measurements (which are repeated under the
same conditions). It is synonymous to reliability.
• Measurements can be both accurate and precise, accurate but not precise,
precise but not accurate, or neither

26. GUESS MY AGE?

27. Significant Figures
• These are digits in a reading that specify the precision of the instrument.
RULES
Rule Example
1. All non – zero digits are significant 11 has 2 significant figures.
98762 has 5 significant figures.
2. Zeroes placed before other digits are not significant 0.012 has 2 significant figures
3. Zeroes placed between other digits are significant 2009 has 4 significant figures
4. Zeroes placed after other digits but behind a decimal point are
significant
1.80 has 3 significant figures

28. 5. When the zeroes in a number are placeholders, write
the number in scientific notation to indicate the number
of significant figures
In the number 2000, it is not clear if the
zeroes are significant or not. To show the
number of significant figures, wrote 2000
in scientific notation:
2 x 103 mean 1 significant figure
only
2.00 x 103 mean 3 significant
figures
Rounding off
A number 1.876 rounded off to three significant digits is 1.88 while the number
1.872 would be 1.87. The rule is that if the insignificant digit (underlined) is more than
5, the preceding digit is raised by 1, and is left unchanged if the former is less than 5.
If the number is 2.845, the insignificant digit is 5. In this case, the convention is
that if the preceding digit is even, the insignificant digit is simply dropped and, if it is
odd, the preceding digit is raised by 1. Following this, 2.845 is rounded off to 2.84
where as 2.815 is rounded off to 2.82.

29. • All measurements are made with the help of instruments.
• Physical quantities obtained from experimental observation always have
some uncertainty. Measurements can never be made perfect. Precision of a
number is often indicated by following it with ± symbol and a second
number indicating the maximum error likely.
• Measured value = (true value + uncertainty) units
What is the length of the fish?
________________________

30. Accurate? Precise? or What?
• A group of boys were
playing darts

31. Boy A pulls of his
stunt first
Accurate? Precise?
or What?

32. Boy B pulls of his
stunt first
Accurate? Precise?
or What?

33. Boy C pulls of his
stunt first
Accurate? Precise?
or What?

34. Boy D pulls of his
stunt first
Accurate? Precise?
or What?

35. Physical Quantities
and Measurements
Errors

36. Errors
• The uncertainty in the measurement of a physical quantity is
called error.
• It is the difference between the true value and the measured value
of the physical quantity.
• Errors may be classified into the following types:
• Systemic Errors
• Random Errors

37. SYSTEMATIC ERROR RANDOM ERROR
Characteristics Constant magnitude; always positive (measurement
greater than actual size) or always negative
(measurement less than actual value)
Magnitude is not constant; can be positive or negative
Source The instrument used:
- Zero error in a micrometer screw gauge
- Change in length of a steel rule or vernier
calipers depending on the surrounding
temperature
The observer:
- Reaction time of the observer who uses a
stopwatch
The physical condition of the surroundings:
- Assumed value of the acceleration due to
gravity maybe higher or lower than the actual
value at the location of the experiment
The main source is the observer:
- Wrong reading of the scale of the scale of the
instrument
- Wrong count of the number of oscillations of
pendulum
- Parallax error: error in a reading due to the wrong
positioning of the eye when reading a scale
- Error due to changing temperature of the
surroundings during the experiment where the
temperature is assumed to be constant
Methods of
reducing or
eliminating
error
- To eliminate zero errors, note the zero error,
and subtract the error from the readings
- Check a measurement by using a different
instrument, for example, use another stopwatch
to check the time measured.
- To reduce random errors, make repeated readings
and calculate the average reading. Discard any
reading that differs significantly from the rest
before finding the average.

38. Take your pulse rate following the steps.
Answer what is being asked below.
• Place your pointer and middle fingers on the inside of your opposite wrist just below
the thumb.
• Don’t use your thumb to check your pulse, as the artery in your thumb can make it
harder to count accurately.
• Once you can feel your pulse, count how many beats you feel in one full minute using a
stop watch.
• Do this 5 times. The first pulse rate is to be labelled ME (since you are the one who got
the results). For the other 4 results, let someone in your household (parents, siblings,
househelp) get your pulse rate following the steps above.
• Please note a normal pulse rate is 80 beats per minute.

39. Where there instances that there is/are random errors? Why did it
happen? How are these obstacles reduced or eliminated?
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
TRIALS LABEL PULSE PER
MINUTE
1st ME
2nd
3rd
4th
5th
Where there instances that there is/are systematic errors? Why did it
happen? How are these obstacles reduced or eliminated?
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________

40. Variance
• It is a way to estimate errors from multiple measurements of a physical
quantity. It is by measuring how wide the points in a data set are spread
about the mean or average.

41. STEPSINCALCULATINGTHE
VARIANCEOFASETOF
MEASUREMENTS

42. Using the sets of pulse rates gathered.
• Determine the following:
• Mean
• Variance
• Standard Deviation