1. The document discusses measurement and quantities, including defining measurement, basic and derived quantities, and units of measurement like meters, seconds, kilograms, etc. 2. It explains scalar and vector quantities, with scalars having only magnitude and vectors having both magnitude and direction. Derived quantities are defined based on basic quantities using formulas. 3. Instruments for measurement like rulers, vernier calipers, and micrometers are described, along with how to read measurements from the scales and calculate measurement uncertainty.

1. CHAPTER 1
QUANTITIES and MEASUREMENTSand
1. Measurement
2. Quantities
• Basic and Derived Quantities
• Scalar and Vector Quantities
Using Your Brain for a Change 1Created by Rozie
3. Dimension
4. Measurement Uncertainly
5. Significant Numbers and Scientific Notation

2. Measurement or to measure is an activity to compare a
quantity with another quantity that is assigned as a unit
1.Measurement
A. The Unit Of Length: metreA. The Unit Of Length: metre
1 metre
“The distance between two marks on a bar of platinum - iridium
alloy that was stored in IBWM in Sevres, France “
Before 1967
After1983
“the path traveled by light in vacuum
during a time interval of 1/299,792,458 s”
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1 metre
From 1967- 1983
“1,650,763.73 times the wavelength of a certain orange spectral line
of atomic krypton-86”
After1983
during a time interval of 1/299,792,458 s”

3. B. The Unit of time: second
“1 second is defined as the time required for exactly
9,192,631,770 oscillations of an isotope cesium -133
atom particle “atom particle “
C. The Unit of Mass: kilogram
“ 1 kg is the mass of a platinum – iridium cylinder kept in
the IBWM, France
D. The Unit of Electric Current: ampere
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D. The Unit of Electric Current: ampere
“ 1 A is the electric current flowing in two long parallel
wires and have distance of 1 m in vacuum space and it
gives force of 2 x 10 -7N/m”

4. E. The Unit of Temperature: kelvin
“1 K is 1/273.16 times temperature of triple point of water “
F. The Unit of Luminous Intensity: candelaF. The Unit of Luminous Intensity: candela
“1 cd is 1/16 of luminous intensity resulted from 1 cm2 of
the blackbody radiation glowing at temperature of frozen
platinum, that is 2046 K “
G. The Unit of Amount of Substance: mole
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“1 mole is the amount of substances that contains 6.02 x
1023 particles “

5. The Prefixes of SI Units
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6. 2. Quantities
“Something that’s measurable and
expressible by number” Basic Quantities
“the physical quantities the units of
which are predetermined”
Quantities
Derived Quantities
“the physical quantities the units of
which are derived from basic quantity
units”
Base of Units
Vector
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Base of have
or haven’t
direction Scalar
Vector
“described by both a magnitude and
a direction”
“described by a magnitude (or
numerical value) alone “

7. Basic Quantities
BASIC QUANTITIES BASIC UNITS
In 1960, scientist at the General Conference of Weight and
Measures adopted the international usage of a metric system of
measurement called International System of Units (abbreviated
as SI)
BASIC QUANTITIES BASIC UNITS
Name Symbol
Length metre m
Mass kilogram kg
Time second s
Temperature kelvin K
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Temperature kelvin K
Luminous Intensity candela cd
Amount of Substance mole mol
electric current ampere A

8. Derived
Quantities
Formula Derived from Basic
quantities
Units
Derived Quantities
t
s
v 
For Example:
Area A= p . l Length m2
Velocity Length and Time m/s
Acceleration Length and Time m/s2
t
s
v 
t
v
a 
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Force F = m . a Mass, Length and Time kg m/s2 = N
Density Mass and Length kg/m3
Work W = F . s Mass, Length and Time kg m2/s2 = J
V
m


9. Vector and Scalar Quantities
Examples of scalars and vectors
Scalar quantity Vector quantity
distance displacementdistance
speed
temperature
energy
power
displacement
velocity
acceleration
force
weight
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mass
density
volume
time
momentum
torque
electric field
magnetic flux density

10. 3. Dimension
Used to describe the method of arrangement of derived
quantities from basic quantities
BASIC QUANTITIES DIMENSIONS
ghv 
BASIC QUANTITIES DIMENSIONS
Length [L]
Mass [M]
Time [T]
Temperature [θ]
Luminous Intensity [J]
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Luminous Intensity [J]
Amount of Substance [N]
electric current [I]

11. Benefit of Dimension:
1. Dimension can be used to check that 2 quantities are homogeneity or
equality. For example: Proof that “Work (W = F . S)” and “kinetic
energy (EK = ½ mv2) ” are equal!
2. To find that a equation is true or false (however, does not guarantee
that the equation is physically correct).that the equation is physically correct).
For example:
Which of these equations could be correct!
a. b. c.
d.
ghv  gv
T
v

asvv 22
0
2

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d.
3. To find dimension or units of unknown quantities in a equation.
For example:
What is dimension of h in the equation E = h f (E = energy, f =
frequency, and h = Planck constant)
asvv 20 

12. Question 1
1. Find the dimension of the derived quantities follow!
a. weight, w (w= m . g) b. Pressure, P ( P= F/A)
c. Electric charge, q (q= I . t) d. Power, P (P= E/t)
2. Find the units (in term of the basic units) and the dimension
of k in the equation
(F= electrostatic force, q= electric charge, and r= distance)
2
21
r
qq
kF 
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3. Find the units (in term of the basic units) and the dimension
of R in the equation
(P= pressure, V= volume, n= amount of substance, and T=
temperature)
nRTPV 

13. The instrument to measure length
1. Ruler
2. Vernier Caliper
Smallest scale value:
1mm
3. Micrometer screw gauge
2. Vernier Caliper
Smallest scale value:
0.1mm
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3. Micrometer screw gauge
Smallest scale value:
0.01mm

14. HOW TO READ A MEASUREMENT FROM THE SCALES ON
THE VERNIER CALIPER and THE MICROMETER
1. Vernier Caliper
a. Type 1a. Type 1
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•Main Scale : 2.3 cm
•Vernier Scale : (2 x 0.01) = 0.02 cm
The Reading is 2.32 cm = 23.2 mm

15. b. Type 2
•Main Scale : 1.9 cm
•Vernier Scale : (6.4 x 0.01) = 0.064 cm
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The Reading is 1.964 cm = 19.64 mm

16. 2. Micrometer Screw Gauge
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•Main Scale : 14.5 mm
•Vernier Scale : (11 x 0.01) = 0.11 mm
The Reading is 14.61 mm = 1.461 cm

17. 4. Measurement Uncertainly (MU)
- General error/ Human error: skill
to use instrument, mistake in read
scale
MU Caused By
- Systematic error: mistake of
instrument calibration, mistake of zero
point, mistake of parallax, mistake of
instrument component, and mistake of
environmental condition (temperature,
atmospheric pressure, air humanity)
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atmospheric pressure, air humanity)
- Random error: electric voltage
fluctuation, Brown movement of
air molecules

18. For single measurement
Absolute
Uncertainly
nstX  2
1
)( 22
1 

XXn
X ii
For Recurrent Measurement
∆X = Absolute Uncertainly
nst = smallest scale value
MU
1
)(1



n
XXn
X ii
n
RU = Relative Uncertainly
X0 = result of the single
n = the sum of recurrent measurement
Xi = the result of quantity measurement of i - th
For single measurement
%100


X
X
RU
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For Recurrent MeasurementRelative
Uncertainly
X0 = result of the single
measurement
%100
0

X
RU
%100


X
X
RU n
X
X i

X The mean of quantity
measurement

19. Reporting the Result of Measurement
• For single measurement:
XXX  0
• For recurrent measurement:• For recurrent measurement:
XXX 
X = physical quantity measured
X0 = result of single measurement
= The mean of quantity measurementX
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= The mean of quantity measurement
∆X = absolute uncertainly
X

20. Sample Problem:
1.The result of a coin diameter measurement
use a vernier caliper is 1.24 cm. Write the
report of result measurement!
Solution:Solution:
D0 = 1.24 cm
½ nst = ½ x 0.01 cm = 0.005 cm
Thus, the diameter of the coin is
DDD  0
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or
cmD )005.024.1( 
%4.0%100
24.1
005.0
 xRUcmD %)4.024.1( 

21. 2. A six times measurement of electric current finds the
reading of 12.8 mA, 12.2 mA, 12.5 mA, 13.1 mA, 12.9
mA, dan 12.4 mA. Write the report of result
measurement aforesaid!
Solution:
I2Ii
Solution:
163.84 mA
148.84 mA
156.25 mA
171.61 mA
166.41 mA
12.8 mA
12.2 mA
12.5 mA
13.1 mA
12.9 mA
1
2
3
4
5
Ii
2Iii
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166.41 mA
153.76 mA
12.9 mA
12.4 mA
5
6
mAIi 9.75 mAIi 71.9602


22. mA
n
I
I i
65.12
6
9.75



14.0
)9.75()71.960(61)( 222
1





IIn
I ii
Thus, the electric current is
14.0
16
)9.75()71.960(6
6
1
1
)(1







n
IIn
I ii
n
mAI )14.065.12( 
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23. 5. Significant Numbers
Exact Numbers “all numbers that are gained from
counting”
EX: “A book has 75 pages”.
Significant Numbers (SN)
SN
“all numbers that
are gained from Consist of
Exact numbers
Estimation number
NUMBERS
EX: “A book has 75 pages”.
Number of 75 is exact number
Using Your Brain for a Change 23Created by Rozie
are gained from
measurement”
Consist of
Estimation number
(“the latest number”)
EX: “The result of a coin diameter measurement use a vernier
caliper is 1.25 cm”. Numbers of 1.25 has 3 SN, numbers of 1
and 2 are exact number, while number 0f 5 is estimation number

24. 1. All number other than zero are SN (Significant Number)
 6.234 has 4 SN
 5.3 has 2 SN
The Significant Numbers Rules
B. The zeroes number on the left hand of numbers other
2. Rules for zeroes number
A. The zeroes number between two numbers other than
zero is SN
• 406 has 3 SN
• 20,0408 has 6 SN
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B. The zeroes number on the left hand of numbers other
than zeroes, is not significant number
• 0.008 has 1 SN
• 0.0123 has 3 SN
• 0.00460 has 3 SN

25. C. The zeroes number on the right hand of numbers other
than zero and behind the decimal point is significant
number.
• 0.4600 has 4 SN
D. The zeroes number on the right hand of numbersD. The zeroes number on the right hand of numbers
other than zero but not behind the decimal point is
not significant number, except if there is a sign like
an underline.
• 25000 has 2 SN
• 25000 has 4 SN
If the number of 25000 is written by scientific notation, so
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If the number of 25000 is written by scientific notation, so
number of significant digits depend of its written.
• 2.5 x 104 has 2 SN
• 2.50 x 104 has 3 SN
• 2.500 x 104 has 4 SN

26. Rules of Significant numbers calculation
1. For Addition or Subtraction
“the result can only one estimation numbers”
• Sample Problem:
a. 273.219 9 is estimation number (EN)
15.5 5 is estimation number15.5 5 is estimation number
8.43 3 is estimation number
------------- +
297.149 (has 3 EN) 297.1 (the end result has one EN)
2. For Multiplication or Division
“the result can only have SN as many as the smallest SN
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“the result can only have SN as many as the smallest SN
between the numbers multiplied”
0.6283 has 4 significant numbers (SN)
2.2 has 2 SN
---------- x
1.8226 has 5 SN, so the end result is 1.8 (has 2 SN)

27. But for multiplication between significant numeral and exact
number “the result can only have SN similar be possessed
by significant numeral”
EX: Thick of a book is 1.25 cm. how many thick of book heap
of 20 piece?
5.125.2 
of 20 piece?
Solution: 1.25 x 20 = 25,0
has 3 SN has 3 SN
3. For Power and Root
“the result can only have SN as many as SN of the numbers
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“the result can only have SN as many as SN of the numbers
that powered or rooted”
5.125.2  1.50 has 3 SN
  25.65.2
2
 6.2 has 2 SN

28. 6. SIGNIFICANT NOTATION
Written of numbers in form: a x 10n with 1 < a <10 and n=
integer
• 120000 1,2 x 105• 120000 1,2 x 105
• 10000 104
• 0.000253 2.53 x 104
• 125 x 10-5 1.25 x 10-3
• 0.00228 x 108 2.28 x 105
Using Your Brain for a Change 28Created by Rozie
• 0.00228 x 108 2.28 x 105