Concepts of Measurement
Basic Fundamental Quantities
SI unit (International
system of units): Is the system of units which is used internationally
to measure three basic physical quantities.
|Basic physical quantity||SI unit|
an international system which is a decimal based system, consequently,
conversions from one unit to another within the metric system can
accomplished by multiplying or dividing by ten or power of ten.
With the exception of temperature, amount of substance and luminous
intensity international other units of measurement that are smaller or
larger than the most commonly used units are expressed by attaching a
prefix to the most commonly used units.
- Giga(G) = 1,000,000,000 (10ˆ9)
- Mega(M) = 1,000,000 (10ˆ6)
- Kilo(K) = 1,000(10ˆ3)
- Hector (h) = 100(10ˆ2)
- Decca(da) = 10(10ˆ1)1
- Deci (d) = 1/10 (10ˆ-1)
- Cent (c) = 1/100(10ˆ-2)
- Mill (m) = 1/1000 (10ˆ-3)
- Micro(μ) = 1/1,000,000(10ˆ-6)
to the thickness of the wood,the eye must always be placed vertically
above the mark being read, in order to avoid errors due to parallax.
- Vernier caliper
- Micrometer screw gauge
main scale is graduated in centimeter (cm) while the vernier scale is
graduated in millimeter (mm).The vernier scale is a short scale 9mm long
divided into 10 equal parts, so that the difference in length between a
vernier division and the main scale division is 0.1mm or 0.01cm.
inside jaws are used to measure the inside diameter while the outside
jaws are used to measure outside diameter.The vernier slides over the
- The main scale reading is recorded. This is the reading which precedes the zero mark of the vernier scale.
vernier scale reading is recorded by reading the mark on it which
coincide with a mark on the main scale (i.e. vernier scale reading x
- The summation of these two readings is the length of the object measured.
is used to measure the diameters of wires and ball bearings. It can
measure small lengths up to about 2.5cm.The diagram below describes the
micrometer screw gauge.
consists of a spindle which is fitted with a graduated thimble. The
screwed portion of a spindle is totally enclosed to protect it from
damage.The pitch of the screw is 0.5mm, so that the spindle moves
through o.o5cm for each complete turn.
anvil and the spindle grip the measured object between them. The
ratchet prevents the user from using undue pressure. The sleeve is
graduated in mm, each graduation represent one complete turn of the
- Sleeve reading is recorded. This gives the units and the first two decimal places in mm.
- Thimble reading is then recorded. This gives the third decimal place (thimble reading x 0.001mm).
- The summation of these two readings gives the diameter of the object under measurement.
- Before use,the faces of anvil and spindle should be wiped clean to remove any dirty particle which would give false readings.
- Check and record for zero error then + or –the correction to the final answer.
|Is the amount of matter contained||Is the force by which the earth pull a body to its centre|
|SI unit is kilogram||SI unit is Newton|
|Doesn’t vary from place to place on the earth’s surface||Varies from place to place on the earth’s surface|
|Measured by beam balance||Measured by a spring balance|
units which are derived from the fundamental quantities. Examples are
volume, density, power, work, energy, weight, frequency etc.
SI units of Derived quantities
|Volume||Cubic meter (mˆ3)|
Basic Apparatus/equipment’s and their uses
is the amount of space occupied by a substance. The SI unit is cubic
meter (mˆ3).Other units used are cubic centimetre (cmˆ3) and litre(l).
are always taken at the level of the bottom of the meniscus or curved
surface of the liquid. Mercury is an exception as its meniscus curves
should be taken to place the eye correctly to avoid parallax errors.
When taking readings, the pipette and burette must be upright and the
cylinder and flask must stand on a horizontal bench otherwise errors may
arise from tilting.
volume of an irregular solid can be determined by measuring the volume
of water displaced in a measuring cylinder directly or with the aid of
an overflow eureka can.
- Poor a known volume of water in a burette(V1)
- Tie a stone with a thread.
- Immerse the tied stone in water holding the thread and record the volume (V2)
- Make sure the stone is totally immersed in water.
- Volume before introducing solid = V1
- Volume after introducing solid = V2
- Volume of irregular solid(V3) = V2 – V1
- Poor water into eureka can up to its spout
- Immerse a well tied stone in water completely
- Collect the overflowed water in the water.
- Use a measuring cylinder to determine the volume of water collected
- When a stone was introduced in an overflow can, water overflowed to the measuring cylinder.
- The volume of water collected is equal to the volume of irregular object(stone)
is the difference between the measured value and the real or actual
value (The difference in reading is known as the error).
- Systematic errors
- Random errors
errors results in the measurement or reading being consistently over
the actual value OR consistently smaller than the actual value.
- Zero error:
Zero Error is caused if the reading shown is Not zero when the true
value is actually zero. This is most probably caused by a flaw in the
instrument for example when using a ruler that has lost its zero scale
due to wear and tear hence causing an error in the measurement of
- Wrong assumptions: For example if you
assume that water boils at 100 degree Celsius but actually its boiling
point is higher if there are impurities in it. (Pure water boils at 100
- Lag of reaction time: For
example in a sports day, when measuring a 100 m running time using a
stopwatch. The observer may not press the stop button exactly when the
foot of the runner touches the finishing line.
- Calibration errors:
Instruments that are not properly calibrated could also cause error and
this has to be put in consideration when writing a report or when there
is an anomaly in reading.
error is caused by the observer who reads the measuring instrument.
Just like the systematic error, there is also positive or negative
error. Positive error is when the reading is bigger than the real value
and negative error is when the reading is smaller than the real value.
- Taking several readings and then find the average.
parallax error by positioning the instrument (meter rule) properly on
the table with the eyes perpendicular to the scale.
instruments can be adjusted to eliminate zero error. For example when
using an ammeter, there is an adjuster to set the indicator to zero
before making any measurement.
- In the case of a ruler,
measurement can be carried out starting from the next clear scale for
example if scale 0.0cm is blurred, we can start measuring the length
from 2.0cm, of course taking the difference of value in consideration
when recording the final reading.
Density and Relative Density
unit of density is kg/mˆ3. Other unit used is g/cmˆ3.Density of regular
solid object can easily be found by direct and easy measurements.-It
involves measuring the mass and calculating the volume as described in
the experiment below.
- The mass of the rectangular block is m.
- The volume of the rectangular block will be calculated by multiplying the obtained length, l height, h and width, w.
- Volume, V = l x h x w, But; Density = mass/volume
- The volume of a material can be obtained by using various methods depending on the shape of the material
- Obtain the mass of the given object using the beam balance.
- Fill water to the measuring cylinder to the volume V₁.
- Immerse the well tied irregular object totally in the cylinder containing water.
- Record the new volume V₂.
- Volume of irregular object = V₂ – V₁
- Mass obtained = M
The Density of a Liquid
Determine the density of a liquid
- Record the mass of the empty beaker m₁ using a beam balance.
- Pour the known volume of kerosene into the beaker by using bur rete, V.
- Record the mass of the beaker and kerosene m₂.
of a substance is the ratio of its density to the density of water.The
density of water has the density of approximately 1.0g/cm³ or 1000kg/m³.
the density of pure water is 1g/cm³, the RD of a substance will be
represented by the same number as its density in g/cm³.RD has no units as its ratio of same quantities.
Application of RD in real life.
- It is the key factor which is considered during the design of various structures and equipment. Eg. ships and planes.
- Density is considered during the selection of materials.
- Density is also considered during the design of equipment used in swimming.