EBOOK_EISBN_COMPLETE_CHAPTER 1_PHYSICAL QUANTITIES AND MEASUREMENT

POLYTECHNIC SERIES

PHYSICAL
QUANTITIES AND

MEASUREMENT

Mohd Sharif Kadir
Rusnani Ali

PHYSICAL
QUANTITIES

AND
MEASUREMENT

MOHD SHARIF KADIR
RUSNANI ALI

Politeknik Sultan Haji Ahmad Shah

Published by
POL/TEKNIK SULTAN HAJI AHMAD SHAH
SEMAMBU
25350 KUANTAN

e ISBN 978-967-2766-26-1

Copyright ©2022, by Politeknik Sultan Haji Ahmad Shah

Materials published in this book of chapter under the copyright of Politeknik Sultan Haji
Ahmad Shah. All rights reserved. No part of this publication may be reproduced or distributed
in any formor by means, electronic, mechanical, photocopying, recording, or otherwise or
stored in a database or retrieval system without the prior written permission of the
publishers.

PREFACE

We are thankful to Allah SWT for His Bless in completing this e-book of chapter physical
quantities and measurement.

This e-book of chapter is formulated to help polytechnic students who are taking the
engineering science course to understand physical quantities and measurement and apply their
knowledge of the subject. The contents of this e-book are arranged based on the latest syllabus
requirements for polytechnics.

This e-book is delivered in a simple way for polytechnics students and direct approach. The e-
book emphasizes notes and examples to guide students in the learning process. It also consists
of progressive exercise at the end of each sub topic. The sentences used is simple and easy to
understand. The e-book arrangement will prove effective in helping students in their studies
and prepare them for their examinations.

Congratulation to all lectures whom involved in writing and editing this e-book, namely Mohd
Sharif Kadir and Rusnani Ali. And special thanks to our Head of Department, Puan Latifah
Sisam in supporting us in this project.

We hope that all polytechnic students will use this e-book of chapter wisely in developing their
science skill and cognitive thinking. Lastly, we hope that everyone enjoy sciences in their life.

Thank you.

Mohd Sharif Kadir
Rusnani Ali

CONTENTS

PHYSICAL QUANTITIES AND MEASUREMENT

1.1 Introduction Page
1.1.1 Base Quantities, Derived Quantities and the
International System (SI) of Units 1
4
1.1.2 Define Scalar and Vector Quantities 5
7
1.2 Standard Form, Scientific Notation and Prefixes
Progressive Exercise 1

1.3 Solve problem of Unit Conversion 9
1.3.1 Convert Metric Units and Customary Units 9
Progressive Exercise 2 13

1.4 Basic Measuring Instruments 15
Progressive Exercise 3 18

1.5 Define Measurement and Error in Measurement 24
1.5.1 Describe Consistency (Precision), Accuracy and Sensitivity 24
1.5.2 Random Errors and Systematic Errors 26
Progressive Exercise 4 29

Answers of Progressive Exercise 34
References 36

PHYSICAL QUANTITIES AND MEASUREMENT

Physical Quantities and
Measurement

1.1 Introduction

1. A physical quantity is quantities that can be measured.
2. Terminology ‘Physical’ something that is real in the sense that it can be seen, felt, etc and

can thus be described in terms of what you observe or perceive.
3. A physical quantity a physical property that can be expressed in number e.g.length 24 m.
4. All physical quantities are measured in units based on the International Systems of units,

which is also commonly known as SI Units.
5. A physical quantity can be categorized into:-

a. Base quantity
b. Derived quantity

1.1.1 Base Quantities, Derived Quantities and the
International System(SI) of Units

Base Quantities

1. A base quantity is a physical quantity that cannot be expressed in term of other physical
quantities.

2. The are seven base quantities which are given table 1.1.

[AUTHOR NAME] 1

PHYSICAL QUANTITIES AND MEASUREMENT

Base Quantity(Symbol) SI Units SI Units (Symbol)
1. Lenght (l) Metre m
2. Mass (m) kg
3. Time (t) kilogram s
4. Temperature ( ) second K
5. Current (I) Kelvin A
6. Amount of Substance (n) Ampere mol
Mole cs
7. Luminous Intensity (Iv) Candela

Table 1: Base quantities and units

Derived Quantities
1. Derived quantities are obtained from a combination of various base quantities and their

unit is determined from the relation between the base quantities and the derived
quantities.

Where:-

2. The SI derived units for these derived quantities are obtained from these equatios and the
seven SI base units. Example of such SI derived units are given table 1.2.

[AUTHOR NAME] 2

PHYSICAL QUANTITIES AND MEASUREMENT

Drived Quantity(Symbol) SI Units SI Units (Symbol)
1. Area (A) Square metre m2
Meter per second
2. Acceleration (a ) m/s2
squared
3. Capacitance (C) farad F

4. Density Kilogram per cubic Kg/m3
meter
5. Energy (E) joule J
6. Electric resistance (R ) ohm Ω
7. Force (F) N
8. Heat (Q ) Newton J
joule
9. Pressure (P) Pa
Pascal (newton per
10. Power (P ) square meter) W
11. Potential difference (V) watt V
12. Volume (V) volt m3
13. Velocity (v) Cubic meter m/s
14. Work (W) meter per econd J
joule

Table 2: Derived quantities and units

International System(SI)

1. International system of units (SI) created by French scientists in 1795.
2. The international system of units (SI) is a system of units of measurement consisting

of seven base units.
3. Mostly widely used system of measurement.

[AUTHOR NAME] 3

PHYSICAL QUANTITIES AND MEASUREMENT

1.1.2 Define Scalar and Vector Quantities

1. Physics deals with many physical quantities, which are diveded into scalars and vectors.
2. A scalar quantity is defined as a quantity that has magnitude only.
3. Vector quantity is defined as a quantity has both magnitude and direction.

Scalars Vectors
• Magnitude and direction
• Magnitude only.
Example:- direction.

• Distance Example:-
• speed • Displacement
• Mass • Velocity
• Time • Weight
• Area • Lift
• Work • Drag
• Temperature • Momentum
• Acceleration

Table 3: Scalar and vector

[AUTHOR NAME] 4

PHYSICAL QUANTITIES AND MEASUREMENT

1.2 Standard Form , Scientific Notation and Prefixes

1. Astronomers, engineers, physicists and many other encouter quantities whose measures
involve very small or very large number.

2. For example, the distance of the earth from the sun is approxinately 144,000,000,000
meters and the distance that light will travel in 1 year is 5,870,000,000,000 meters.

3. Prefix and standard form reduces the need to write many zeros
4. There are two ways to express very large or small numbers.

a) Metric prefixes
b) Scientifik notification (standard form)

Metric Prefixes
Prefixes is a symbol that place in front of a unit. The prefix will indicate a multiple of the unit.

Example 1
Caculate this numbers 5870,000,000,000 to metric prefixes.

Solution:

5,870,000,000,000 = 5.87 T

Scientific Notification (standard form)

Many measurements in modern scientific fields involve very large and very small numbers. It is
trouble to write many zeroes for very large and very small numbers.
Example: Speed of light = 300 000 000 m/s

Wave length of violet light = 0.00000038 m

[AUTHOR NAME] 5

PHYSICAL QUANTITIES AND MEASUREMENT

Example 2
Caculate this numbers 5870,000,000,000 to standard form

Solution:
5,870,000,000,000 = 5.87 T = 5.87 x 1012 @ 5.87e12

Example 3

The distance from planet Earth to Sun is 1.5108 km Find the distance in
megameter(Mm).

Solution:

1Mm  106 m 1km  103 m
1.5 108 km  1.5 108 km 103 m  1Mm

1km 106 m
 1.5 105 Mm

Example 4
Change numbers 3, 00,000,000 to standard form.

Solution:

3 00 000 000 = 3.0 x 100 000 000
= 3.0 x 108 m/s (standard form)

[AUTHOR NAME] 6

PHYSICAL QUANTITIES AND MEASUREMENT

Example 5

Express the following as standard form:-

a. 4 000 c. 0.0000125

b. 3450000 d. 0.0034

Solution: b. 3450000
= 3.45 x 106
a. 4 00000
= 4.0 x 105 d. 0.0034

c. 0.0000125 = 3.4 x 10-4
= 1.25 x 10-5

ogressive PROGRESSIVE EXERCISE 1 Exerciseogressive
Exercise Example

Progressive Exercise

1) Complete the table with accurate fact:

Item Define

Physical quantities

Base quantities

[AUTHOR NAME] 7

PHYSICAL QUANTITIES AND MEASUREMENT

Derived quantities

The International
System (SI) of units

2) Complete the table below with suitable answer. VECTOR QUANTITY
SCALAR QUANTITY

Scalar quantity is ………………………………… Vector quantity is ………………………………

……………………………………………………. ………………………………..………….……….

…………………………………………………… …………………………………..……….……….

Example (2 example) Example (2 example)

[AUTHOR NAME] 8

PHYSICAL QUANTITIES AND MEASUREMENT

1.3 Solve Problem of Unit Conversion

1. Anytime when we solve physics problem we need to use all the variables in the same
system of unit.

2. In certain specific situation, the value of physical quantities need to be change from one
unit to another.

3. When you solve phaysics problem: remember to check the units before you substitute
all the numbers into the equations.

4. Change in unit of physical quantities are neccery in cases where the calculations involve
the use of formula. What this is the unit of every quantity in the formula must be uniform.

1.3.1 Convert Metric Units and Customary Units

Convert Metric Units
1. The metric system is a system of measurement that involves measuring length, mass and
volume in their respective metric units.
2. The standard units (SI) for measuring length are kilimeters, meters and centimeters; weight
are kilograms, grams and miligrams, volune are liters and mililiters.

[AUTHOR NAME] 9

PHYSICAL QUANTITIES AND MEASUREMENT

Large Units Small Units

Metric Metric Metric Metric Multiple
Prefix Symbol
Tera Multiple Prefix Symbol 1 = 100
Giga T 1012 0.1 = 10-1
Mega Unit (gram, meter, liter) 0.01=10-2
Kilo 0.001 = 10-3
G 109 deci- d 0.000001 = 10-6
hecto-
M 1,100,000 = 106 centi- e 10-9
10-12
k 1,000 = 103 Mili- m

h 100 = 102 micro- μ

deca- da 10 = 101 nano- n
1 = 100 pico- p
Unit (gram, meter, liter)

Table 4(a): Metric prefixes

Length Time Mass
1 Km ----- 1000 m 1 hour ----- 60 min 1 kg ----- 1000 g
1 cm ----- 100 cm 1 min ------ 60 s 1 g ----- 1000 mg
1 cm ----- 10 mm 1 hour ----- 3600 s 1 tonne ----- 1000 kg
1 m ------ 1000 mm
1 kg ----- 1 L

Force Work/Energy Power
1 kN ----- 1000 N 1 KJ ----- 10000 J 1 kW ----- 1000 W

Volume Area
1 L ----- 1000 ml 1 km2 ----- 100 ha
I L ----- 1000 cm3 1 km2 - 1,000,000 m2
1m3 ----- 1000 L 1 m2 ---- 10,000 cm2

Table 4(b): Metric prefixes

[AUTHOR NAME] 10

PHYSICAL QUANTITIES AND MEASUREMENT

Example 6

Change the following quantities to the units shown :

a. 11 km to m b. 35 km to 2 c. 1.5 h to s d. 34 km/h to m/s

e. 210 ⁄ 3 to ⁄ 3 f. 100 ⁄ 2 to ⁄ 2

Solution:

a. 11 km to m b. 35 2 to 2
1000
= 35 2 (100)2 2
= 11 km x 1 (1)2 2
= 11,000 m
= 350,000 2

c. 1.5 h to s d. 34 km/h to m/
3600 s 1000 1 ℎ

= 1.15 h x 1 h = 34 ℎ 1 3600
= 4140 s = 9.44 ⁄

e. 210 ⁄ 3 ⁄ 3 f. 100 ⁄ 2 to ⁄ 2
1 (100)2 2
= 0.21 ⁄ 3 (1)3 3
1000 = 100 2 100 (1)2 2
= 210 x 1 (100)3 3 = 10,000 ⁄ 2

= 11,000 m

[AUTHOR NAME] 11

PHYSICAL QUANTITIES AND MEASUREMENT

Convert Customary Units

1. The customary system of measurement, also called the U.S. Customary Systemis based on
the English system of measurement.

2. The conversion metric unit and customary units can be done. The units relate to
measurement of lenght, weight and capacity.

Example 7

Change the following quantities to the units shown.

a. 29 in to cm b. 27 kg to pound

c. 14 gallon to liter d. 60 miles/h to km/h

Solution:

a. 29 in to cm b. 27 kg to pounds
2.54 2.2

= 29 in x 1 in = 27 kg x 1 kg
= 73.66 cms = 59.4 pound

c. 14 gallon to liter mile
3.79 d. 60 h /ℎ

= 14 gallon x 1 gallon 1
= 53.06 liter = 60 mile/h x 0.621
= 96.62 km/h

[AUTHOR NAME] 12

PHYSICAL QUANTITIES AND MEASUREMENT

PROGRESSIVE EXERCISE 2

1. Convert metric unit. b) 450 000 m2 to km2
a) 10 km to m

c) 800 km/h to m/s d) 2.575 m3 to cm3

e) 2905 mg to kg f) 2.52 hr to s

[AUTHOR NAME] 13

g) 4.51L/min to L/hr PHYSICAL QUANTITIES AND MEASUREMENT
h) 250 kg/m3 to g/cm3

i) 75 mg/min to g/hr j) 500 g/cm3 to kg/m3

2. Convert customary unit. b) 54 yd to ft
a) 28 inches to ft d) 2 ft 6 in to cm
f) 85 ft2 to m2
c) 20 km to mile

e) 24 ft 3 in to m

[AUTHOR NAME] 14

3. Temperature conversion PHYSICAL QUANTITIES AND MEASUREMENT
a) 20 0C to F b) 66 0C to F
d) 36.5 F to C
c) 25 F to C

1.4 Basic Measuring Instruments

The following are three types of instruments to measure the length of an object:-
a. Meter Ruler
b. Vernier Calipers
c. Micrometer Screw Gauge

Meter Ruler
1. A meter rule is used to measure medium lengths i.e. o to 1m. it has an accuracy of 0.1
cm.
2. All measurements of length using the ruler have to be recorded accurate to 0.1 cm. for
example, a length of 5 cm will have been recorded as 5.0 cm.

[AUTHOR NAME] 15

PHYSICAL QUANTITIES AND MEASUREMENT

Figure 1 : Measurement of length
Vernier Calipers

1. Vernier calipers to measure the internal or external diameter of an object.
2. It is accurate to 0.01 cm, a pair of Vernier calipers consists of a main scale and a Vernier

Scale as shown in the diagrams below.
3. The outside jaws, are used to measure the outer dimensions of an object and the inner

jaws for the inner.

Figure 2 : Measurement of round object by using vernier calipers
[AUTHOR NAME] 16

PHYSICAL QUANTITIES AND MEASUREMENT
Measuring Using the Vernier Calipers

1. Keep the body to be measured between the fixed jaw and mobile jaw without pressure
on it.

2. The main scale reading.
3. The division of the Vernier that coincides with any division on the main scale is also

noted. This is the Vernier scale reading.
4. Then, the measurement of the object will be, main scale reading + (Vernier scale

reading x least count)
5. Here, least count = Value of One Main Scale Division / Total Number of Division on

the Vernier Scale
6. The units of measurement is in millimeter (mm).

Figure 3 : Measurement of objects

[AUTHOR NAME] 17

PHYSICAL QUANTITIES AND MEASUREMENT

PROGRESSIVE EXERCISE 3

1. Find the readings of the vernier calipers below. Answer
No. Figure

Main Scale : _________
a) Vernier Scale : _________

Final : _________

Main Scale : _________
b) Vernier Scale : _________

Final : _________

Main Scale : _________
Vernier Scale : _________
c)

Final : _________

[AUTHOR NAME] 18

PHYSICAL QUANTITIES AND MEASUREMENT

Main Scale : _________
Vernier Scale : _________
d) Final : _________

Main Scale : _________
e) Vernier Scale : _________

Final : _________

[AUTHOR NAME] 19

PHYSICAL QUANTITIES AND MEASUREMENT

Main Scale : _________
Vernier Scale : _________
f)
Final : _________

2. Find the zero error and the correct reading of the vernier calipers below.
a) b)

Zero error : _____________ Main scale : ______________
Vernier scale : ______________
Final : ______________

[AUTHOR NAME] 20

PHYSICAL QUANTITIES AND MEASUREMENT
Micrometer Screw Gauge

1. Used to measure the diameter of small wire or thickness of a thin object.
2. To measure even smaller lengths, micrometer is used as it has an even smaller precision

i.e. 0.001 cm or 0.01 mm.
3. Before taking measurements, again we are going to look for zero error.

Figure 4 : A Micrometer screw gauge
Measuring using the micrometer screw gauge

1. The object whose diameter is to be measured is placed between anvil and spindle.
2. The ratchet which is a kind of knob is turned to tighten spindle until a ‘tick’ is hear.

[AUTHOR NAME] 21

PHYSICAL QUANTITIES AND MEASUREMENT

Example 8

Determine actual readings on each gauge:

Measuring Instrument Range Precision
Measuring Tape 0–5m 0.1 cm
metre Rule Giga 0–1m 0.1 cm
Vernier Calipers 0 – 15 cm 0.01 cm
Micrometer screw gauge 0 – 2.5 cm 0.001 cm
`

Table 5 : Measurement of instruments

[AUTHOR NAME] 22

PHYSICAL QUANTITIES AND MEASUREMENT

Ruler Vernier Caliper Micrometer Screw
Measuring Tape 0–5m Gauge

0.9 cm 0.92 cm 0.1 cm
0.922 cm

`

Figure 5 : Measurement of thickness a pencil

[AUTHOR NAME] 23

PHYSICAL QUANTITIES AND MEASUREMENT

1.5 Define Measurement and Error in Measurement

1. All measurement in science are attempts to determine the true and actual value of the
relevant physical quantities.

2. Nature of measurement to measure a physical quantity is to make an acceptable estimate
of the true and actual.

Figure 6 : Error in measurement

1.5.1 Describe Consistency(Precision), Accuracy and Sensitivity
Consistency(Precision)

1. Consistency is the ability of an instrument in measuring a quantity in a consistent manner
with only a small relative deviation between readings.

2. The consistency of a reading can be indicated by its relative deviation.
Accuracy

1. The accuracy of a measurement is the approximation of the measurement to the actual
value for a certain quantity pf physics.
[AUTHOR NAME] 24

PHYSICAL QUANTITIES AND MEASUREMENT
2. The measurement is more accurate if its number of significant figure increase.
3. Smaller percent of error more accurate from bigger percent of error.
4. The accuracy of a measurement can be increased by:

 taking a number of repeat readings to calculate the mean value of the reading.
 Avoiding the end errors or zero errors.
 Taking into account the zero and parallax errors.
 Using more sensitive equipment such as a Vernier caliper to replace a ruler.
 The difference between precision and accuracy can be shown by the spread of

shooting of a target.

Figure 7 : Accuracy and Precision

Sensitivity
1. The sensitivity of an instrument is its ability to detect small changes in the quantity that is
being measured.
2. Thus, a sensitive instrument can quickly detect a small change in measurement.
3. Measuring instruments that have smaller scale parts are more sensitive.
4. Sensitive instruments need not necessarily be accurate.

[AUTHOR NAME] 25

PHYSICAL QUANTITIES AND MEASUREMENT

1.5.2 Random Errors and Systematic Errors

1. Error is the difference between the actual value of a quantity and the value obtained in
measurement. There are two main types of errors:-
a. Random errors.
b. Systematic errors.

Random Errors Systematic Errors
• Random errors because they are
• No random but constant.
unpredictable.
• They arise when observers • Due to the equipment being
used – e.g. a ruler with zero
estimate the last figure of a error.
reading on an instrument.
• Cannot be reduced by
• Minimized by averaging a large averaging, but they can be
number of readings. eliminated if the sourcer of the
errors are known.
• Example:
- parallax error (Human) • Example:-
- Counting’s errors - zero error(Instrument)
- Natural errors - Improper use of instrument
- Errord from instrument
- Wrong assumption

Figure 8 : Random and systematic error

[AUTHOR NAME] 26

PHYSICAL QUANTITIES AND MEASUREMENT
Systematic vs. Random Error
The figure 9 below illustrates the distinction between systematic and random errors.

Figure 9 : Distinction between systematic and random error
Parallax error
One form of scale-rading error that often afflicts beginners in the science laboratory is
fairure to properly align the eye with the part of the scale you are reading. This given
rise to parallax error. Parallax refers to the change in the apparent position of an object
when viewed from different points.
To avoid parallax error

 The eye must be positioned vertically above the mark on the scale.
 Several readings and the average must be taken.

Figure 10 : Parallax error

[AUTHOR NAME] 27

PHYSICAL QUANTITIES AND MEASUREMENT

Zero Error
A zero error arise when the measuring instrument does not start from exactly zero. Zero
errors are consistently present in every reading of a measurement. The zero error can be
positive or negative.
Systematic error can be reduced by:

 Conducting the experiment with care.
 Repeating the experiment by using different instruments

Figure 11 : Positive and negative error
Calculating Error

1. Since equipment used in an experiment can only report a measured value with a certain
degree of accuracy, calculating the extent to which a measurement deviates from the
value accepted by the scientific community is often helpful in gaging the accuracy of
equipment.

2. Such a calculation is referred to as the percent error of a measurement and is
represented by the following formula:

Percentage of Error  Experiment al Result - Accepted Value 100%
Accepted Value

[AUTHOR NAME] 28

PHYSICAL QUANTITIES AND MEASUREMENT

Example 9

Calculate error for measurement, accepted value and experimental value 9.

Solution:

Percentage of Error  Experiment al Result - Accepted Value 100%
Accepted Value

% Error  9 -10 100%

10

 10%

PROGRESSIVE EXERCISE 4

1. The following micrometre screw gauges have no zero error. Determine actual readings on each gauge:

No. Figure Answer

Sleeve : ___________
Thimble : ___________
a) Final reading : __________

[AUTHOR NAME] 29

PHYSICAL QUANTITIES AND MEASUREMENT

Sleeve : ___________
b)

Thimble : ___________
Final reading : __________

Sleeve : ___________
c) Thimble : ___________

Final reading : __________

[AUTHOR NAME] 30

PHYSICAL QUANTITIES AND MEASUREMENT

Sleeve : ___________
d) Thimble : ___________

Final reading : __________

2. The following micrometer screw gauges have zero error as indicated in each case. Determine the
actual readings on each gauge:

No. Figure Answer

Sleeve : ___________

a) Thimble : ___________
zero error = -0.47mm
Final reading : __________

[AUTHOR NAME] 31

PHYSICAL QUANTITIES AND MEASUREMENT

Sleeve : ___________
b) Thimble : ___________

Final reading : __________

Zero error = -0.21mm

Sleeve : ___________
c)

Thimble : ___________
Zero error = + 0.01mm

Final reading : __________

[AUTHOR NAME] 32

PHYSICAL QUANTITIES AND MEASUREMENT

d)
Sleeve : ___________
Thimble : ___________
Final reading : __________

Zero error = + 0.55mm

[AUTHOR NAME] 33

ANSWERS PHYSICAL QUANTITIES AND MEASUREMENT

PROGRESSIVE ECERCISE 2 f) = 9,072 s
g) = 270.6 L/hr
1. Convert metric unit. h) = 0.25 g/cm3
i) = 4.5 g/h
a) = 10,000 m j) = 500,000 kg/m3
b) = 0.45 km2
c) = 222.22 m/s d) = 76.2 cm
d) = 2,575,000 cm3 e) = 7.391 m
e) = 2.905 x 10-3 f) = 7.65 m2
c) = -3.885 0C
2. Convert customary unit. d) = 2.5 0C
a) = 2.333 ft
b) = 162 ft [AUTHOR NAME] 34
c) = 12.43 mile

3. Temperature conversion
a) = 68 0F
b) = 150.8 0F

PROGRESSIVE ECERCISE 3

1.

a) 10.02 cm
b) 5.31 cm
c) 7.05 cm
d) 1.16 cm
e) 9.03 cm
f) 3.73

2. a) zero error = + 0.03 cm PHYSICAL QUANTITIES AND MEASUREMENT
b) final reading = 1.03 cm

PROGRESSIVE ECERCISE 4

1. b) Final reading : 09.49 mm
a) Final reading : 12.18 mm d) Final reading : 12.50 mm
c) Final reading : 11.98 mm

2. : 410 mm b) Final reading : 12.39 mm
: 9.48 mm d) Final reading : 11.95 mm
a) Final reading
c) Final reading

[AUTHOR NAME] 35

REFERENCES

Azia Idayu Awang, Azhari Zakaria, Hardyta Bujang Pata, Khairani Yaakub, Noor
Affandee.(2015). Engineering Science, Polytechnic Series. Shah Alam:Oxford Fajar Sdn.
Bhd.
Ir. Dr. Latifah Malek.(2014). SPM Physics Learning Through Diagrams. Shah Alam: UG
Press Sdn. Bhd.
Lee, B.H. and Poh, L.Y.(2016). Physics for Matriculation Semester 1 Fifth Edition. Shah
Alam: Oxford Fajar Sdn. Bhd.
Yew Kok Leh, Koay Kheng Chuan, Chang See Leong. (2014). Focus Physics SPM Form 4.5.
Seri Kembangan: Pelangi Sdn. Bhd.
https://www.cyberphysics.co.uk/practical/skills/micrometer.htm
http://one-school.net/notes/physics/spm_physics_definition.html
https://circuitglobe.com/accuracy-and-precision.html
https://www.quora.com/How-can-we-measure-the-LC-of-a-vernier-caliper
http://physics401.one-school.net/2009/01/140-measurements-and-error.html
https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_%28
Analytical_Chemistry%29/Quantifying_Nature/Significant_Digits/Uncertainties_in_Measure
ments

36