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Objectives• To identify mm, cm as sub-multiples of the

metre and km as a multiple of the metre• To state the SI units of length, area and

volume• To use the metre rule and measuring tape

correctly to take measurements• To use the vernier calipers correctly to take

measurements and read the measurements from diagrams, to take into account zero error if any

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Objectives• To identify the use of the micrometer screw

gauge (workings & readings taken by instruments are not required)

• To choose the appropriate instruments (measuring tape, metre rule, micrometer screw gauge or vernier calipers) for measuring length, diameter or thickness

• To measure the area of irregular figures using squared paper

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Objectives• To identify the different apparatus for

measuring the volumes of liquids, e.g. volumetric flask, measuring cylinder, pipette, burette and know their degree of accuracy

• To use the measuring cylinder and Eureka can to find the volume of irregular objects

• To state the precautions to take when using the metre rule and vernier calipers and when taking readings from measuring cylinder

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Science is based on empiricism- a search for knowledge based on

experimentation and observation.

Observations can be either qualitative or quantitative.

Qualitative observations describe while quantitative observations measure.

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In science, quantitative observations are preferred because they can be clearly communicated.

They are normally measured according to standard procedures.

Measuring allows us to make accurate observations that are required in scientific work as well as in everyday uses.

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Instruments have been invented to make more accurate measurements.

Some instruments which you will use to measure with are the- metre rule- vernier calipers- burette- pipette- measuring cylinder.

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Physical Quantities, SI Units and Prefixes

A physical quantity is a quantity which can be measured.Examples of some of them are length, volume, mass, time, temperature, etc.

A non-physical quantity is one which cannot be measured.Examples of some of them are beauty, kindness, humour, sadness, untidiness, etc.

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Since 1960, scientists from different parts of the world have agreed to adopt a single system of units called the SI Units (SI stands for Système International d’Unités in French). This system is an adaptation of the metric system.

There are altogether seven basic quantities: length, mass, time, electric current, thermodynamic temperature, luminous intensity and amount of substance.

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All the other physical quantities are derived from the seven basic quantities.For example, area, volume, speed.

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The International System of Units (SI units)

Out of these seven basic quantities, only five will be covered at your level.They are length, mass, time, electric current and temperature.

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Prefixes are used to change them by factors of ten into smaller or bigger units.

Prefix Symbol Factor

micro 10-6 one millionthmilli m 10-3 one thousandthcenti c 10-2 one hundredthdeci d 10-1 one tenthkilo k 103 one thousand timesmega M 106 one million times

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Class Work:

Convert the following to SI unit:

(a) 24 km = _________ m(b) 55 cm = _________ m(c) 56 MJ = _________ J(d) 9.8 g = _________ kg(e) 35 mg = _________ kg(f) 77 s = _________ s

24000

0.55

56000000

0.0098

0.000077

0.000035

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Measurement of Length

Length is the distance between two points.

SI unit: metre, m

1 m = 100 cm1 cm = 10 mm

Short distance - cm or mmLong distance - km

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Metre rule

This instrument is commonly used in the laboratory to measure the lengths of objects such as wires or distance between two points.

Metre rules are graduated in millimetres therefore readings taken from a metre rule should be given to the nearest millimetre.

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If a metre rule is thick, it should be placed so that the scale is as near to the object as possible so that readings can be taken without parallax error.

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When taking readings from the metre rule, make sure that the line of vision is perpendicular to the scale so as to avoid parallax error.

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Parallax error

For accurate measurements using the metre rule, the eye must be placed vertically above the markings of the metre rule to avoid parallax error.

Parallax errors are errors due to the incorrect positioning of the eye and the object not touching the markings of the scale.

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Parallax errors can be avoided by

- placing the eye vertically above themarking on the scale to be read.

- placing the metre rule on its edge besidethe object to be measured so that the scaleis touching it.

- using a thin rule so that the scale istouching the object to be measured.

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Calipers

External Caliper- accuracy of 0.1 cm

Internal Caliper- accuracy of 0.1 cm

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External Calipers

Measuring the externaldiameter.

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Internal Calipers

Measuring the internaldiameter.

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Vernier Calipers

The vernier calipers is most commonly used for accurate measurement of up to ±0.1 mm or ±0.01 cm.

By means of a vernier scale, the second decimal place in cm can be obtained without having to estimate fractions of a division using the eye.

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Vernier calipers have a set of inside jaws, outside jaws and a tail.

The inside jaws are used for measuring internal diameters, the outside jaws is for measuring externaldiameter while the tail isfor measuring depth.

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Step 1: Grip the object using the outside orinside jaws of the calipers.

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Step 2: Read the last division on the mainscale that has passed the zero line ofthe vernier scale.

Step 3: Look for a line on the vernier scalewhich is exactly opposite to any lineon the main scale, count this line,starting from the zero-line (of thevernier scale). This number is thenext decimal place in your answer.

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Step 2 (3.1 cm)

Step 3 (3.18 cm)

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_______ cm

4 5

0 5 10

_______ cm

8 9

0 5 10

To Java Applet

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Zero error

Before using the vernier calipers, the jaws must be closed to check if there is zero error.

When the zero marking on the vernier scale is not in line with the zero marking on the main scale, the distance between the two markings is the zero error.

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If the zero marking of the vernier scale is to the right of the zero marking on the main scale when the jaws are closed, the zero error is positive.

Zero error= 0.09 cm

0 1

0 5 10

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0 1

0 5 10

If the zero marking of the vernier scale is to the left of the zero marking on the main scale when the jaws are closed, the zero error is negative..

Zero error= -0.01 cm

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0 1

0 5 10

4 5

0 5 10

Zero error= 0.09 cm

Observed reading= 4.03 cm

Accurate reading= 4.03 - 0.09 cm= 3.94 cm

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0 1

0 5 10

4 5

0 5 10

Zero error= -0.01 cm

Observed reading= 4.03 cm

Accurate reading= 4.03 - (-0.01) cm= 4.04 cm

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Micrometer Screw Gauge

The micrometer screw gauge is used to give very accurate measurements of length up to 25 mm. It has an accuracy of ±0.01 mm (or ±0.001 cm).

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Measurement of Area

Area is a measure of the extent of a surface.

SI unit: square metre, m2

1 km2 = 1000000 m2

1 cm2 = 0.0001 m2

1 mm2 = 0.000001 m 0.000001 m22

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The area of regular surfaces can be calculated using formulae.

Area of a Square = l2

Area of a Rectangle = l bArea of a Trapezium = ½ (a + b) hArea of a Circle = r2

l

l

l

b

r

a

b

h

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For irregular surfaces, their areas can be estimated by first dividing them into small unit squares and counting them.

An incomplete square is counted as one if its area is more than or equal to half of the area of a unit square.

If areas of the incomplete square are less than half, they are not counted.

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Area of 1 square = 1 cm2

No. of squares counted = 15Total area estimated= 15 1= 15 cm2

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Measurement of Volume

Volume is a Volume is a measure of the space occupied by a substance.

SI unit: cubic metre, m3

1 km3 = 100000000 m3

1 cm3 = 0.000001 m3

1 mm3 = 0.00000001 m m33

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Some objects have regular shapes, for example, books, basketballs, pyramids and soft-drink cans. The volume of regular-shaped objects can be calculated using formulae.

Volume of a cube = l3

Volume of a rectangular block = l b hVolume of a sphere = 4/3 r3

Volume of a cylinder = r2 h

l

h

bl

l

l

r

r

h

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Instruments commonly used in the laboratory for measuring volume of liquids include the measuring cylinder, burette, pipette and volumetric flask.

Liquids are drawn into a pipetteby means of a pipette filter up to|a mark showing the exact volumeof a liquid in the pipette. Suckingby mouth is not recommendeddue to safety and hygiene reasons.

pipette burette

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When using a measuring cylinder,readings are taken to the nearesthalf-division.

When reading, the measuring cylindermust not be held in hand. It must beplaced on a horizontal bench.

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Meniscus reading

When you pour water into a measuring cylinder and place it on the bench or any flat surface, you will observe that the water surface is curved.

The meniscus of most liquids curves downwards. The correct way to read the meniscus is to position the eye at the same level as the meniscus.

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The mark corresponding to the bottom of the meniscus is taken as the reading.

The meniscus of mercury curves upwards. The correct reading is the mark that corresponds to the top of the meniscus.

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When taking readings from the measuring cylinder, the bottom of the water meniscus was read horizontally at the eye level to avoid parallax error.

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Measuring the volume of a small irregular-shaped object

1. Partly fill a measuring cylinder withwater. Observe and record the initialwater level, V0, in the measuring cylinder.

2. Tie the irregular-shaped object with apiece of string. Lower it gently into themeasuring cylinder so that it is completelycovered with water. Observe and recordthe final water level, V1.

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3. The volume of the irregular-shaped object,V, is the difference between the two waterlevel readings andis given V = V1 - V0.

V1

V0

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Measuring the volume of a small irregular-shaped object that floats on water

- use a sinker(an object that sinks)

V = V1 - V0

V0 = Level of weightV1 = Level of weight and sinker

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Measuring the volume of a large irregular-shaped object

1. Fill thedisplacement canwith water untilexcess water flowsout of its spout intoa beaker. Removethe beaker when water stops flowing

intoit.

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2. Place an empty measuring cylinder belowthe spout of the displacement can. Tie theirregular-shapedobject with a pieceof string. Lower itgently into the canuntil it iscompletelyimmersed in thewater.

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3. When the water stops flowing into themeasuring cylinder, observe and recordthe volume of water displaced by theobject and collected in the measuringcylinder. The volume

of the water in themeasuring cylinderis equal to the volumeof the irregular-shapedobject.

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References

Tho Lai Hong, Ho Peck Leng, Goh Ngoh Khang, (2001), Interactive Science 1, Pan Pacific Publications.

Chan Kim Fatt, Eric Y K Lam, Lam Peng Kwan, Loo Poh Lim, (2000), Science Adventure, Federal Publications.

Chuen Wee Hong, Lee Khee Boon, Hilda Tan, Ruth Chellappah, Koh Thiam Seng, Yap Kueh Chin, (2000), EPB.