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QB003 – SCIENCEQB003 – SCIENCE(BRIDGING)(BRIDGING)

CHAPTER 1: CHAPTER 1: UNITS AND UNITS AND

MEASUREMENTMEASUREMENT

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UNDERSTANDING OF UNDERSTANDING OF UNITS & MEASUREMENTUNITS & MEASUREMENT

State the base quantity, derived quantity and its unitState the base quantity, derived quantity and its unit Express quantities using prefixesExpress quantities using prefixes Express quantities using scientific notationExpress quantities using scientific notation Solve problems involving conversion of unitsSolve problems involving conversion of units Measure physical quantities using appropriate Measure physical quantities using appropriate

equipmentsequipments Explain types of experimental errorsExplain types of experimental errors

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INTRODUCTION

Physical quantities

Base quantities Derived quantities

Prefixes Scientific notation(standard form

Scalar quantities Vector quantities

Measurement

Error

Systematic error Random error

CONCEPTUAL MAP

BASE QUANTITIESBASE QUANTITIES

Base QuantitiesBase Quantities are pare physical quantities that cannot be defined in term of hysical quantities that cannot be defined in term of other quantities.other quantities.

Scientific measurement using SI units (International System Units)Scientific measurement using SI units (International System Units). .

Base Base QuantitiesQuantities

SymbolSymbol SI UnitSI Unit Symbol of Symbol of

SI unitSI unit

LengthLength ll metermeter mm

MassMass mm kilogramkilogram kgkg

TimeTime tt secondsecond ss

TemperatureTemperature TT KelvinKelvin KK

Electric Electric currentcurrent

II ampereampere AA

Table 1.1 Shows five base quantities and their respective SI units

DERIVED QUANTITIIESDERIVED QUANTITIIES Derived QuantitiesDerived Quantities are physical quantities derived from combination are physical quantities derived from combination

of base quantities through multiplication or division or bothof base quantities through multiplication or division or both

Derived QuantitiesDerived Quantities SymbolSymbol Relationship with base quantitiesRelationship with base quantities Derived unitsDerived units

AreaArea AA Length x LengthLength x Length mm22

VolumeVolume VV Length x Length x LengthLength x Length x Length mm33

DensityDensity ρρ MassMassLength x Length x LengthLength x Length x Length

kg/mkg/m33

VelocityVelocity vv DisplacementDisplacementTimeTime

m/sm/s

AccelerationAcceleration aa VelocityVelocityTimeTime

m/sm/s22

ForceForce FF Mass x AccelerationMass x Acceleration NN

WorkWork WW Force x DisplacementForce x Displacement JJ

EnergyEnergy EEpp

EEkk

Mass x gravity x high @Mass x gravity x high @½ x mass x velocity x velocity½ x mass x velocity x velocity

JJ

PowerPower PP Force x DisplacementForce x DisplacementTimeTime

WW

PressurePressure p p ForceForceAreaArea

N/mN/m 2 2

Table 1.2 shows some of the derived quantities and their respective derived units

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Scalar Quantities & Vector QuantitiesScalar Quantities & Vector Quantities Scalar quantitiesScalar quantities are physical quantities that have are physical quantities that have magnitude onlymagnitude only Vector quantitiesVector quantities physical quantities that have physical quantities that have magnitudemagnitude and and

directiondirection

Scalar quantitiesScalar quantities Vector quantitiesVector quantities

LengthLength WorkWork DisplacementDisplacement

SpeedSpeed TemperatureTemperature VelocityVelocity

MassMass DensityDensity AccelerationAcceleration

TimeTime EnergyEnergy MomentumMomentum

AreaArea VolumeVolume ForceForce

Table 1.3 shows a list of some examples of scalar and vector quantities

PREFIXESPREFIXES

PrefixesPrefixes are used to simplify the are used to simplify the description of physical quantities that description of physical quantities that are either very big or very small.are either very big or very small.

PrefixPrefix SymbolSymbol ValueValue

teratera TT 10101212

gigagiga GG 101099

megamega MM 101066

kilokilo kk 101033

hektohekto hh 101022

dekadeka dada 1010

desidesi dd 1010-1-1

sentisenti cc 1010-2-2

milimili mm 1010-3-3

mikromikro HH 1010-6-6

nanonano nn 1010-9-9

pikopiko PP 1010-12-12

Table 1.4 Lists some commonly used SI prefixes

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STANDARD FORMSTANDARD FORMStandard formStandard form or or scientific notationscientific notation is used to express magnitude in is used to express magnitude in a simpler way. In scientific notation, a numerical magnitude can be a simpler way. In scientific notation, a numerical magnitude can be written as :written as :

A x 10A x 10nn,, where 1 where 1 ≤ A < 10 and ≤ A < 10 and nn is an integer is an integer

Example 1.1 :

For each of the following, express the magnitude using a scientific notation.(I) The mean radius of the balloon = 100 mm(II) The mass of a butterfly = 0.0004 kg

Solution:

The mean radius of the balloon= 100 mm= 1.0 x 102 mm

The mass of a butterfly= 0.0004 kg= 4.0 x 10-4 kg

CONVERSION UNITSCONVERSION UNITS

Example 1.2 Example 1.2 : :

Convert 3.5 kilometer to meter.Convert 3.5 kilometer to meter.

SolutionSolution1km = 101km = 1033m = 1000mm = 1000m

therefore therefore 3.5 km = 3.5 km 3.5 km = 3.5 km xx 1000m 1000m

1 km1 km = 3.5 = 3.5 1000 m 1000 m = = 3500 m3500 m

Illustrates the usage of prefixesIllustrates the usage of prefixes

Example 1.3Example 1.3::

Express 0.0005 Mg in gExpress 0.0005 Mg in g

SolutionSolution1kg = 101kg = 1033g = 1000gg = 1000g

1Mg = 101Mg = 1066g = 1000 000gg = 1000 000g

therefore therefore 0.005 Mg = 0.0005 Mg 0.005 Mg = 0.0005 Mg xx 1000 000g 1000 000g

1 Mg1 Mg = 0.0005 = 0.0005 1000 000 g 1000 000 g = = 500 g500 g

Example 1.4Example 1.4::

Change 50 msec to sec.Change 50 msec to sec.

SolutionSolution1 msec = 101 msec = 10-3-3 sec =0.001sec sec =0.001sec

ThereforeTherefore50 msec = 50 msec x 50 msec = 50 msec x 1 sec 1 sec

0.001 msec 0.001 msec = 50 x 1 sec= 50 x 1 sec 0.001 0.001 = 50 x 10= 50 x 10-3 -3 secsec = 50 x 10= 50 x 10-2 -2 secsec = = 0.05 sec0.05 sec

Contoh 1.5Contoh 1.5::

Convert 0.075 kW to mW.Convert 0.075 kW to mW.

SolutionSolution

kW → W → mWkW → W → mW

ThereforeTherefore

kW → W = 0.075 kW kW → W = 0.075 kW 1000 W 1000 W 1 1 kW kW = 0.075 = 0.075 1000 W 1000 W

= 75 W= 75 W

W W → → mW = 75 W mW = 75 W 1000 mW 1000 mW 1 W 1 W

= = 75 000 mW75 000 mW

CONVERSION UNITSCONVERSION UNITS

Example 1.6Example 1.6 : :

Change 60 km/j to m/s.Change 60 km/j to m/s.

SolutionSolution 1 km = 1000m1 km = 1000m 60 km/j = 60 km x 1000 m x 1 hr60 km/j = 60 km x 1000 m x 1 hr 1 hour = 60 minute1 hour = 60 minute 1 hr 1 km 3600 s 1 hr 1 km 3600 s 1 minute = 60 sec = 60 x 1000 m1 minute = 60 sec = 60 x 1000 m 3600 s3600 s

= = 16.67 m/s16.67 m/s

Example 1.7Example 1.7 : :

The density of pure water is 1000 kg mThe density of pure water is 1000 kg m-3-3, what is its density in g cm, what is its density in g cm-3 -3 ??

SolutionSolution 1 kg = 1000 g1 kg = 1000 g 1 m = 100 cm1 m = 100 cm

1000 kg = 1000 kg x 1000 g x ( 1 m x 1 m x 1 m )1000 kg = 1000 kg x 1000 g x ( 1 m x 1 m x 1 m ) mm33 m m33 1 kg 100 cm 100 cm 100 cm 1 kg 100 cm 100 cm 100 cm

= 1000 x 1000 g = 1000 x 1000 g 1 00 00 00 cm1 00 00 00 cm33

= 1 g cm= 1 g cm-3-3

EXERSICEEXERSICEConvert the following unitsConvert the following units

1.1. 120 cm in unit meter (m)120 cm in unit meter (m)

2.2. 550 mg in unit gram (g)550 mg in unit gram (g)

3.3. 5600 mV in KV5600 mV in KV

4.4. 9.81 m/s in unit km/j9.81 m/s in unit km/j

5.5. 8500 cm8500 cm22 in m in m22

6.6. 908 g/cm908 g/cm33 in kg/m in kg/m33

7.7. 45 g/cm45 g/cm22 in kg/m in kg/m22

Micrometer screw gaugeMicrometer screw gauge

Vernier calipersVernier calipers

MEASUREMENT INSTRUMENTS

RulerRuler

ERROR IN MEASUREMENTERROR IN MEASUREMENT An error is the difference between the measured value and the An error is the difference between the measured value and the

actual value.actual value. There are 2 main types of errors in measurementThere are 2 main types of errors in measurement

Systematic errors

• May be due to the error in calibration of instruments • Zero error is due to non-zero reading when the actual reading should be zero

Random errors

• Due to mistakes made by observer when taking measurement either through incorrect positioning of the eye (parallax) or the instruments when taking measurement

• It may also occur when there is a sudden change of environmental factors like temperature, air circulation and lighting

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