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Using Your Brain for a Change 1Created by Rozie

2. Using Your Brain for a Change 2Created by Rozie
CHAPTER 1
BESARAN dan SATUAN
3. Pengukuran
1. Besaran
2. Dimensi
4. Ketidakpastian Pengukuran
5. Angka Penting dan Notasi Ilmiah

3. Using Your Brain for a Change 3Created by Rozie
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: 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
From 1967- 1983
“1,650,763.73 times the wavelength of a certain orange spectral line
of atomic krypton-86”
After1983
“the path traveled by light in vacuum
during a time interval of 1/299,792,458 s”

4. Using Your Brain for a Change 4Created by Rozie
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 “
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
“ 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 -7
N/m”

5. Using Your Brain for a Change 5Created by Rozie
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: 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
“1 mole is the amount of substances that contains 6.02 x
1023
particles “

6. Using Your Brain for a Change 6Created by Rozie
Awalan Satuan

7. Using Your Brain for a Change 7Created by Rozie
2. Quantities
(Besaran)“Something that’s measurable and
expressible by number”
Quantities
Basic (pokok)
Derived (turunan)
“the physical quantities the units of
which are predetermined”
“the physical quantities the units of
which are derived from basic quantity
units”
Berdasarkan satuan
Berdasarkan
kepemilikan
arah Skalar
Vector
“described by both a magnitude and
a direction”
“described by a magnitude (or
numerical value) alone “

8. Using Your Brain for a Change 8Created by Rozie
Basic Quantities
BASIC QUANTITIES BASIC UNITS
Name Symbol
Length (l) metre m
Mass (m) kilogram kg
Time (t) second s
Temperature (T) kelvin K
Luminous Intensity (I) candela Cd
Amount of Substance (n) mole mol
electric current (i) ampere A
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)

9. Using Your Brain for a Change 9Created by Rozie
Derived
Quantities
Formula Derived from Basic
quantities
Units
Area A= p . l Length m2
Velocity Length and Time m/s
Acceleration Length and Time m/s2
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
Derived Quantities
t
s
v =
t
s
v =
t
v
a =
For Example:
V
m
=ρ

10. Using Your Brain for a Change 10Created by Rozie
Vector and Scalar Quantities
Examples of scalars and vectors
Scalar quantity Vector quantity
distance
speed
temperature
energy
power
mass
density
volume
time
displacement
velocity
acceleration
force
weight
momentum
torque
electric field
magnetic flux density

11. Using Your Brain for a Change 11Created by Rozie
3. Dimension
Used to describe the method of arrangement of derived
quantities from basic quantities
BASIC QUANTITIES DIMENSIONS
Length [L]
Mass [M]
Time [T]
Temperature [θ]
Luminous Intensity [J]
Amount of Substance [N]
electric current [I]
ghv ρ=

12. Using Your Brain for a Change 12Created by Rozie
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).
For example:
Which of these equations could be correct!
a. b. c.
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)
ghv ρ= λgv =
T
v
=λ
asvv 22
0
2
+=

13. Using Your Brain for a Change 13Created by Rozie
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)
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)
2
21
r
qq
kF =
nRTPV =

14. Using Your Brain for a Change 14Created by Rozie
The instrument to measure length
1. Ruler
3. Micrometer screw gauge
2. Vernier Caliper
Smallest scale value:
1mm
Smallest scale value:
0.1mm
Smallest scale value:
0.01mm

15. Using Your Brain for a Change 15Created by Rozie
HOW TO READ A MEASUREMENT FROM THE SCALES ON
THE VERNIER CALIPER and THE MICROMETER
1. Vernier Caliper
a. Type 1
•Main Scale : 2.3 cm
•Vernier Scale: (2 x 0.01) = 0.02 cm
The Reading is 2.32 cm = 23.2 mm

16. Using Your Brain for a Change 16Created by Rozie
b. Type 2
•Main Scale : 1.9 cm
•Vernier Scale: (6.4 x 0.01) = 0.064 cm
The Reading is 1.964 cm = 19.64 mm

17. Using Your Brain for a Change 17Created by Rozie
2. Micrometer Screw Gauge
•Main Scale : 14.5 mm
•Vernier Scale: (11 x 0.01) = 0.11 mm
The Reading is 14.61 mm = 1.461 cm

18. Using Your Brain for a Change 18Created by Rozie
4. Measurement Uncertainly (MU)
MU Caused by
- General error/ Human error: skill
to use instrument, mistake in read
scale
- 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)
- Random error: electric voltage
fluctuation, Brown movement of
air molecules

19. Using Your Brain for a Change 19Created by Rozie
For single measurement
For Recurrent Measurement
Absolute
Uncertainly
MU
Relative
Uncertainly
nstX ×=∆ 2
1
1
)( 22
1
−
Σ−Σ
=∆
n
XXn
X ii
n
RU = Relative Uncertainly
X0 = result of the single
measurement
n = the sum of recurrent measurement
Xi = the result of quantity measurement of i - th
For single measurement
For Recurrent Measurement
%100
0
×
∆
=
X
X
RU
%100×
∆
=
X
X
RU
∆X = Absolute Uncertainly
nst = smallest scale value
n
X
X iΣ
=
=X The mean of quantity
measurement

20. Using Your Brain for a Change 20Created by Rozie
Reporting the Result of Measurement
• For single measurement:
XXX ∆±= 0
• For recurrent measurement:
XXX ∆±=
X = physical quantity measured
X0 = result of single measurement
= The mean of quantity measurement
∆X = absolute uncertainly
X

21. Using Your Brain for a Change 21Created by Rozie
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:
D0 = 1.24 cm
½ nst = ½ x 0.01 cm = 0.005 cm
Thus, the diameter of the coin is
or
DDD ∆±= 0
cmD )005.024.1( ±=
%4.0%100
24.1
005.0
== xRUcmD %)4.024.1( ±=

22. Using Your Brain for a Change 22Created by Rozie
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:
163.84 mA
148.84 mA
156.25 mA
171.61 mA
166.41 mA
153.76 mA
12.8 mA
12.2 mA
12.5 mA
13.1 mA
12.9 mA
12.4 mA
1
2
3
4
5
6
Ii
2
Iii
mAIi 9.75=Σ mAIi 71.9602
=Σ

23. Using Your Brain for a Change 23Created by Rozie
mA
n
I
I i
65.12
6
9.75
==
Σ
=
Thus, the electric current is
14.0
16
)9.75()71.960(6
6
1
1
)( 222
1
=
−
−
=
−
Σ−Σ
=∆
n
IIn
I ii
n
mAI )14.065.12( ±=

24. Using Your Brain for a Change 24Created by Rozie
5. Significant Digits
Significant Numbers (SN)
SN
“all numbers that
are gained from
measurement”
Consist of
Exact numbers
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
Exact Numbers
NUMBERS
“all numbers that are gained from
counting”
EX: “A book has 75 pages”.
Number of 75 is exact number

25. Using Your Brain for a Change 25Created by Rozie
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
than zeroes, is not significant number
• 0.008 has 1 SN
• 0.0123 has 3 SN
• 0.00460 has 3 SN
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

26. Using Your Brain for a Change 26Created by Rozie
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 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
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

27. Using Your Brain for a Change 27Created by Rozie
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 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
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)

28. Using Your Brain for a Change 28Created by Rozie
However, 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?
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
that powered or rooted”
5.125.2 =
5.125.2 = 1.50 has 3 SN
( ) 25.65.2
2
= 6.2 has 2 SN

29. Using Your Brain for a Change 29Created by Rozie
6. SCIENTIFIC NOTATION
Written of numbers in form: a x 10n
with 1 < a <10 and n=
integer
• 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