PHYSICAL QUANTITIES AND MEASUREMENT by PolisasLib3

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

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 ebook 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

Page 1.1

1.2

1.3

1.4

1.5

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

1.1.2

Define Scalar and Vector Quantities

Standard Form, Scientific Notation and Prefixes

Progressive Exercise 1

Solve problem of Unit Conversion

1.3.1

Convert Metric Units and Customary Units

Progressive Exercise 2

Basic Measuring Instruments

Progressive Exercise 3

Define Measurement and Error in Measurement

1.5.1

Describe Consistency (Precision), Accuracy and Sensitivity

1.5.2

Random Errors and Systematic Errors

Progressive Exercise 4

Answers of Progressive Exercise

References

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]

PHYSICAL QUANTITIES AND MEASUREMENT Base Quantity(Symbol)

SI Units

SI Units (Symbol)

1. Lenght (l)

Metre

2. Mass (m)

kilogram

3. Time (t)

second

4. Temperature ( )

Kelvin

5. Current (I)

Ampere

6. Amount of Substance (n)

Mole

mol

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]

PHYSICAL QUANTITIES AND MEASUREMENT Drived Quantity(Symbol)

SI Units

SI Units (Symbol)

Square metre

2. Acceleration (a )

Meter per second squared

m/s2

3. Capacitance (C)

farad

Kilogram per cubic meter

Kg/m3

5. Energy (E)

joule

6. Electric resistance (R )

ohm

Ω

7. Force (F)

Newton

8. Heat (Q )

joule

9. Pressure (P)

Pascal (newton per square meter)

10. Power (P )

watt

11. Potential difference (V)

volt

12. Volume (V)

Cubic meter

13. Velocity (v)

meter per econd

m/s

joule

1. Area (A)

4. Density

14. Work (W)

Table 2: Derived quantities and units

International System(SI) 1.

International system of units (SI) created by French scientists in 1795.

The international system of units (SI) is a system of units of measurement consisting of seven base units.

Mostly widely used system of measurement.

[AUTHOR NAME]

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 only.

Magnitude and direction direction.

Example:-

•

Distance

•

Displacement

•

speed

•

Velocity

•

Mass

•

Weight

•

Time

•

Lift

•

Area

•

Drag

•

Work

•

Momentum

•

Temperature

•

Acceleration

Table 3: Scalar and vector

[AUTHOR NAME]

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

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]

PHYSICAL QUANTITIES AND MEASUREMENT

Example

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

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

1 Mm  10 6 m

1 km  10 3 m

1.5  10 8 km  1.5  10 8 km 

10 3 m 1 Mm  1km 10 6 m

 1.5  10 5 Mm

Example

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]

PHYSICAL QUANTITIES AND MEASUREMENT

Example

Express the following as standard form:a. 4 000

0.0000125

b. 3450000

0.0034

Solution:

4 00000

= 3.45 x 106

= 4.0 x 105

d. 0.0034

0.0000125 = 1.25 x 10-5

ogressive Exercise

3450000

= 3.4 x 10-4

PROGRESSIVE EXERCISE 1

Exerciseogressive

Progressive Exercise 1)

Complete the table with accurate fact: Item

Define

Example

Physical quantities

Base quantities

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

Derived quantities

The International System (SI) of units

Complete the table below with suitable answer. SCALAR QUANTITY

VECTOR QUANTITY

Scalar quantity is …………………………………

Vector quantity is ………………………………

…………………………………………………….

………………………………..………….……….

……………………………………………………

…………………………………..……….……….

Example (2 example)

[AUTHOR NAME]

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]

PHYSICAL QUANTITIES AND MEASUREMENT

Large Units Metric Prefix Tera

Metric Symbol T

Small Units

10 12

Metric Metric Prefix Symbol Unit (gram, meter, liter) deci-

0.1 = 10-1

Multiple

Multiple 1 = 100

Giga

109

Mega

1,100,000 = 10 6

centi-

0.01=10-2

Kilo

1,000 = 103

Mili-

0.001 = 10-3

hecto-

100

= 102

micro-

0.000001 = 10-6

deca-

= 101

nano-

10-9

= 10 0

pico-

10-12

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 m ------ 1000 mm Force 1 kN ----- 1000 N Volume

1 tonne ----- 1000 kg 1 kg ----- 1 L

Work/Energy 1 KJ ----- 10000 J

Power 1 kW ----- 1000 W

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]

PHYSICAL QUANTITIES AND MEASUREMENT

Example

Change the following quantities to the units shown : a. 11 km to m b.

35 km to 𝑚2

𝑔 e. 210 𝑘𝑔⁄𝑚3 to ⁄𝑐𝑚3

1.5 h to s

34 km/h to m/s

100 𝑁⁄𝑐𝑚2 to 𝑘𝑁 ⁄𝑚2

Solution:

11 km to m

35 𝑘𝑚2 to 𝑚2

1000 𝑚 = 11 km x 1 𝑘𝑚

(100)2 𝑚2 = 35 𝑘𝑚 𝑥 (1)2 𝑘𝑚2

= 11,000 m

= 350,000 𝑚2

1.5 h to s = 1.15 h x

3600 s 1h

= 34

210 𝑘𝑔⁄𝑚3 𝑡𝑜 𝑔⁄𝑐𝑚3 = 0.21 𝑚⁄𝑐𝑚3

1000 𝑔 = 210 x 1 𝑘𝑔

𝑘𝑚 1000 𝑚 1ℎ 𝑥 𝑥 ℎ 1 𝑘𝑚 3600 𝑠

= 9.44 𝑚⁄𝑠

= 4140 s

34 km/h to m/𝑠

(1)3 𝑚3 𝑥 (100)3 𝑐𝑚3

100 𝑁⁄𝑐𝑚2 to 𝑘𝑁 ⁄𝑚2 = 100

𝑁 1 𝑘𝑁 (100)2 𝑐𝑚2 𝑥 𝑥 𝑐𝑚2 100 𝑁 (1)2 𝑚2

= 10,000 𝑘𝑁 ⁄𝑚2

= 11,000 m

[AUTHOR NAME]

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

Change the following quantities to the units shown. a.

29 in to cm

27 kg to pound

14 gallon to liter

60 miles/h to km/h

Solution:

29 in to cm

= 29 in x

2.54 𝑐𝑚 1 in

= 73.66 cms c.

= 53.06 liter

= 27 kg x

2.2 𝑝𝑜𝑢𝑛𝑑 1 kg

= 59.4 pound

14 gallon to liter = 14 gallon x

27 kg to pounds

3.79 𝑙𝑖𝑡𝑒𝑟 1 gallon

mile 𝑡𝑜 𝑘𝑚/ℎ h

= 60 mile/h x

1𝑘𝑚 0.621 𝑚𝑖𝑙𝑒

= 96.62 km/h

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

PROGRESSIVE EXERCISE 2

1. Convert metric unit. a) 10 km to m

c) 800 km/h to m/s

e) 2905 mg to kg

b) 450 000 m2 to km2

d) 2.575 m3 to cm3

f) 2.52 hr to s

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

g) 4.51L/min to L/hr

h) 250 kg/m3 to g/cm3

i) 75 mg/min to g/hr

j) 500 g/cm3 to kg/m3

Convert customary unit. a) 28 inches to ft

b) 54 yd to ft

c) 20 km to mile

d) 2 ft 6 in to cm

e) 24 ft 3 in to m

f) 85 ft2 to m2

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

Temperature conversion a) 20 0C to F

b) 66 0C to F

c) 25 F to C

d) 36.5 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

Vernier Calipers

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]

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]

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]

PHYSICAL QUANTITIES AND MEASUREMENT

PROGRESSIVE EXERCISE 3 1.

Find the readings of the vernier calipers below.

No.

Figure

Answer

Main Scale a)

Vernier Scale : _________ Final

: _________

Main Scale b)

: _________

Vernier Scale : _________ Final

Main Scale

: _________

Vernier Scale : _________ c) Final

: _________

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

Main Scale

: _________

Vernier Scale : _________ d)

Final

: _________

Main Scale

: _________

Vernier Scale : _________ Final

: _________

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

Main Scale

: _________

Vernier Scale : _________ f) Final

: _________

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

Zero error : _____________

Main scale

: ______________

Vernier scale

: ______________

Final

: ______________

[AUTHOR NAME]

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]

PHYSICAL QUANTITIES AND MEASUREMENT

Example

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]

PHYSICAL QUANTITIES AND MEASUREMENT

Ruler Measuring Tape

Micrometer Screw Gauge

Vernier Caliper 0–5m

0.1 cm 0.9 cm

0.92 cm

0.922 cm `

Figure 5 : Measurement of thickness a pencil

[AUTHOR NAME]

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]

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]

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 • •

Random errors because they are unpredictable. They arise when observers estimate the last figure of a reading on an instrument.

Systematic Errors •

No random but constant.

•

Due to the equipment being used – e.g. a ruler with zero error. Cannot be reduced by averaging, but they can be eliminated if the sourcer of the errors are known. Example:- zero error(Instrument) - Improper use of instrument - Errord from instrument - Wrong assumption

• •

Minimized by averaging a large number of readings.

•

Example: - parallax error (Human) - Counting’s errors - Natural errors

•

Figure 8 : Random and systematic error

[AUTHOR NAME]

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]

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.

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]

PHYSICAL QUANTITIES AND MEASUREMENT

Example

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

Solution:

Percentage of Error 

% Error 

9 - 10

10  10%

Experiment al Result - Accepted Value  100% Accepted Value

 100%

PROGRESSIVE EXERCISE 4 1. The following micrometre screw gauges have no zero error. Determine actual readings on each gauge: No.

Figure

Answer

Sleeve

: ___________

Thimble

: ___________

Final reading

: __________

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

Sleeve

: ___________

Thimble

: ___________

Final reading

: __________

Sleeve

: ___________

Thimble

: ___________

Final reading

: __________

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

Sleeve

: ___________

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

: ___________

Thimble

: ___________

zero error = -0.47mm Final reading

: __________

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

Sleeve

: ___________

Thimble

: ___________

Final reading

: __________

Zero error = -0.21mm

Sleeve

: ___________

Thimble

: ___________

Zero error = + 0.01mm Final reading

: __________

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

d) Sleeve

: ___________

Thimble

: ___________

Final reading

: __________

Zero error = + 0.55mm

[AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

ANSWERS PROGRESSIVE ECERCISE 2 1.

Convert metric unit. a) = 10,000 m

= 9,072 s

b) = 0.45 km2

g) = 270.6 L/hr

c) = 222.22 m/s

= 0.25 g/cm3

d) = 2,575,000 cm3

= 4.5 g/h

e) = 2.905 x 10-3

= 500,000 kg/m3

= 76.2 cm

Convert customary unit. a) = 2.333 ft b) = 162 ft c) = 12.43 mile

e) = 7.391 m f)

= 7.65 m2

Temperature conversion a) = 68 0F

c) = -3.885 0C

b) = 150.8 0F

d) = 2.5 0C

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 [AUTHOR NAME]

PHYSICAL QUANTITIES AND MEASUREMENT

2. a) zero error = + 0.03 cm

b) final reading = 1.03 cm

PROGRESSIVE ECERCISE 4

1. a) Final reading : 12.18

b) Final reading

: 09.49 mm

c) Final reading

: 11.98 mm

d) Final reading

: 12.50 mm

a) Final reading

: 410 mm

b) Final reading

: 12.39 mm

c) Final reading

: 9.48 mm

d) Final reading

: 11.95 mm

[AUTHOR NAME]

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

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SULTAN HAJI AHMAD SHAH