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Measuring Length & Volume. 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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Measuring Length & Volume

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Length & Volume


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.


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.


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

- Micrometer screw gauge.


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.


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.


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


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.


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

Prefix Symbol Factor

micro  10-6 one millionth

milli m 10-3 one thousandth

centi c 10-2 one hundredth

deci d 10-1 one tenth

kilo k 103 one thousand times

mega M 106 one million times


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








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


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.


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.


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.


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.


Parallax errors can be avoided by

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

- placing the metre ruler on its edge beside the object to be measured so that the scale is touching it.

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



External Caliper- accuracy of 0.1 cm

Internal Caliper- accuracy of 0.1 cm


External Calipers

Measuring the externaldiameter.


Internal Calipers

Measuring the internaldiameter.


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.


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.


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).


Measurement of Volume

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

SI unit: cubic metre, m3

1 km3 = 1000 000 000 m31 cm3 = 0.000 001 m31 mm3 = 0.000 000 001 m3











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 = l3Volume of a rectangular block = l  b  hVolume of a sphere = 4/3 r3Volume of a cylinder =  r2 h




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 filler up to|a mark showing the exact volumeof a liquid in the pipette. Suckingby mouth is not recommendeddue to safety and hygiene reasons.


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.


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.


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.


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


Measuring the volume of a small irregular-shaped object

1. Partly fill a measuring cylinder with water. Observe and record the initial water level, V0, in the measuring cylinder.

2. Tie the irregular-shaped object with a piece of string. Lower it gently into the measuring cylinder so that it is completely covered with water. Observe and record the final water level, V1.




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


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

- use a sinker (an object that sinks)


Measuring the volume of a large irregular-shaped object

1. Fill the displacement can with water until excess water flows out of its spout into a beaker. Remove the beaker when water stops flowing into it.


2. Place an empty measuring cylinder below the spout of the displacement can. Tie the irregular-shaped object with a piece of string. Lower it gently into the can until it is completely immersed in the water.


3. When the water stops flowing into the measuring cylinder, observe and record the volume of water displaced by the object and collected in the measuring cylinder. The volume of the water in the measuring cylinder is equal to the volume of the irregular-shaped object.