MEASUREMENT
The Concepts of Measurement
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Explain the concepts of measurement
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is the process of assigning numbers to observations or events.
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Importance of Measurements in Real Life
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State the importance of measurement in real life
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Measurements are so often taken for granted, we sometimes do not appreciate the grand
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importance measurements play in our lives. On a baseline level, measurements fall into the
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categories of weight, area, volume, length and even temperature. While we look at these various
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categories as stoic forms of mathematical measurements, a closer examination of things we do in
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everyday life reveals their clear importance.
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If you are ill (whether a serious or minor illness) you need to take
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your medicine and take it in the proper amount. If you take too little or too much then you are
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not going to get the proper benefit from it.
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Cooking of all forms is based on proper attention to measurement. Can you
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bake a chicken at 600 degrees? Well, you can but the results would be pretty catastrophic! Could
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you may a cup of tea by dipping a tea bag into a teaspoon of warm water?
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. Now, how important could measurements be when selecting clothes? After
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all, to look good in clothing the main thing you need to pay attention to is style, right? Well, if
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you weigh 200lbs you aren't going to look stylish in an extra small shirt. Clothing is all based on
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size and proper fitting which are, of course, variants of measurement.
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The importance of measurements may not necessarily reveal itself when you
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play sports but it is there in a big way. If you want to throw a runner out at first or make a 30
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yard touchdown pass then you really need to be accurate and comes from a clear sense of depth
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If you have to be at school at 9am what time would you have to leave in
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the morning if you are at your friend's house. Often we do not have an exact answer so we need
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to make an estimation which is essentially a guess of measurement.
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Keeping yourself warm or cool.
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If the temperature outside dips or increases you have to make
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an adjustment on your thermostat in order to remain at a safe and healthy temperature.
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Understanding the measurement scale of a thermostat is critical in this regard or else you may
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find yourself feeling rather uncomfortable.
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Is that object too heavy to pick up by yourself or do you need to use
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something to lift it? Some may think this is not important but it is pretty easy to hurt yourself if
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you lift objects that are too heavy.
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Just how many clothes can you fit in a dresser or closet without it
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becoming too crammed? Without a clear concept of capacity you might find yourself pouring an
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entire half gallon of orange juice into a small glass!
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The ability to tell time is all based on measurement principles. Whether you are
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using a digital clock or an hourglass these devices measure the passage of time. Now, imagine
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how chaotic the world would be if if was impossible to measure the passage of time.
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How much weight is too much for a plane to take off or a car to move
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efficiently? How much fuel is needed to reach a certain point and how long will it take to get
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somewhere? Yes, measurements play a significant part in transportation.
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This was saved for last because it is the common theme that is found in all the
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multitude of reasons for the importance of measurements. Measurements provide structure and
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remove the chaos that would result without any congruent method of understanding weight,
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Basic Fundamental Quantities
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Define a fundamental quantity
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Is any character which can be measured by an instrument.
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is the standard which is used to explain measurement of a body.Eg; kilogram, metre,
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are numbers that we need to describe the world around us, which we
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cannot express in terms of "simpler," more basic
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. Here is an example: My weight is
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, because it depends on how much stuff makes up my body.
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Three Basic Fundamental Quantities of Measurement
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Mention three basic fundamental quantities of measurement
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Basic f undamental quantities
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are physical quantities from which other physical quantities are
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derived from. This includes three quantities namely
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The S.I Unit of Fundamental Quantity
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State the S.I unit of fundamental quantities
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(International system of units): Is the system of units which is used internationally to
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measure three basic physical quantities.
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SI units of fundamental quantities
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Is an international system which is a decimal based system, consequently, conversions from one
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unit to another within the metric system can accomplished by multiplying or dividing by ten or
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: With the exception of temperature, amount of substance and luminous intensity
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international other units of measurement that are smaller or larger than the most commonly used
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units are expressed by attaching a pr efix to the most commonly used units.
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Giga(G) = 1,000,000,000 (10ˆ9)
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Mega(M) = 1,000,000 (10ˆ6)
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Deci (d) = 1/10 (10ˆ -1)
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Mill (m) = 1/1000 (10ˆ-3)
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Micro(µ) = 1/1,000,000(10ˆ -6)
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Appropriate Instruments for Measuring Fundamental Quantities
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Use appropriate instruments for measuring fundamental quantities
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Length is the distance between two points, objects or space.The SI unit of length is
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Other commonly used units are
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The instrument used to measure length is the
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How to read the metre rule:
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Owing to the thickness of the wood,the eye must always be placed
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vertically above the mark being read, in order to avoid errors due to parallax.
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Measuring of length (diameter) of small objects
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The diameter of small objects is measured by using two instruments:
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is the instrument used to measure length to the accuracy of
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measure lengths to the range of 1.0cm to about 12.0cm.The figur e below describe the structure of
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The main scale is graduated in centimeter (cm) while the vernier scale is graduated in millimeter
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(mm).The vernier scale is a short scale 9mm long divided into 10 equal parts, so that the
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difference in length between a vernier division and the main scale division is 0.1mm or 0.01cm.
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The inside jaws are used to measure the inside diameter while the outside jaws are used to
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measure outside diameter.The vernier slides over the main scale.
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The main scale reading is recorded. This is the reading which precedes the zero mark of
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The vernier scale reading is recorded by reading the mark on it which coincide with a
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mark on the main scale (i.e. vernier scale reading x 0.01cm).
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The summation of these two readings is the length of the object measured.
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A micrometer screw gauge:
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Is an instrument used to measure length to the accuracy
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It is used to measure the diameters of wires and ball bearings. It can
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measure small lengths up to about 2.5cm.The diagram below describes the micrometer screw
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It consists of a spindle which is fitted with a graduated thimble. The screwed portion of a spindle
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is totally enclosed to protect it from damage. The pitch of the scr ew is 0.5mm, so that the spindle
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moves through o.o5cm for each complete turn.
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The anvil and the spindle grip the measured object between them. The ratchet prevents the user
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from using undue pressure. The sleeve is graduated in mm, each graduation represent one
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complete turn of the screw.
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How to read a micrometer screw gauge:
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Sleeve reading is recorded. This gives the units and the first two decimal places in mm.
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Thimble reading is then recorded. This gives the third decimal place (thimble reading x
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The summation of these two readings gives the diameter of the object under
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Precautions when using a micrometer screw gauge.
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Before use,the faces of anvil and spindle should be wiped clean to remove any dirty
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particle which would give false r eadings.
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Check and record for zero error then + or –the correction to the final answer.
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Mass of a body is the amount of matter it contains. The SI unit of mass is
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The mass of a body doesn t change from place to place. The instrument used to measure mass is
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Difference between mass and weight:
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Is the amount of matter contained Is the force by which the earth pull a body to its centre
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SI unit is kilogram SI unit is Newton
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Doesn t vary from place to place on the earth s surface Varies from place to place on the earth s surface
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Measured by beam balance Measured by a spring balance
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Is the gap between two occasions or events.The SI unit of time
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(s). Other units used are
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minutes (min), hour(h),day etc.
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The instruments for measuring time are
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Explain derived quantities
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are units which are derived from the fundamental quantities. Examples are
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volume, density, power, work, energy, weight, fr equency etc.
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The S.I Units of Derived Quantities
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State the S.I. units of derived quantities
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SI units of Derived quantities
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Volume Cubic meter (mˆ3)
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Basic Apparatus/equipment's and their uses
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Basic Apparatus/Equipments Used for Measurement
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Describe basic apparatus/equipments used for measurement
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Volume is the amount of space occupied by a substance. The SI unit is cubic meter (mˆ3).Other
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units used are cubic centimetre (cmˆ3) and litre(l).
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Instruments used to measure the volume of liquids:
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Measuring cylinder-used for measuring or pouring out various liquids.
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Measuring flask and pipette are used for getting fixed pre-determined volume.
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Burette-used to deliver any required volume up to its total capacity.
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How to read volume measuring instruments (precautions).
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Readings are always taken at the level of the bottom of the meniscus or curved surface of the
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liquid. Mercury is an exception as its meniscus curves downwards.
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Care should be taken to place the eye correctly to avoid parallax errors. When taking readings,
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the pipette and burette must be upright and the cylinder and flask must stand on a horizontal
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bench otherwise errors may arise from tilting.
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Measuring volume of irregular objects.
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The volume of an irregular solid can be determined by measuring the volume of water displaced
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in a measuring cylinder directly or with the aid of an overflow eureka can.
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Aim: To measure the volume of an irregular object.
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By using a measuring cylinder directly
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Materials and apparatus: Irregular object eg; stone, thread, measuring cylinder, eureka can and
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Poor a known volume of water in a burette(V1)
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Tie a stone with a thread.
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Immerse the tied stone in water holding the thread and record the volume (V2)
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Make sure the stone is totally immersed in water.
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Volume before introducing solid = V1
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Volume after introducing solid = V2
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Volume of irregular solid(V3) = V2 – V1
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Poor water into eureka can up to its spout
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Immerse a well tied stone in water completely
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Collect the overflowed water in the water.
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Use a measuring cylinder to determine the volume of water collected
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When a stone was introduced in an overflow can, water overflowed to the measuring
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The volume of water collected is equal to the volume of irregular object(stone)
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Sources of Errors in Measurement
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Identify sources of errors in measurement
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Error is the difference between the measured value and the real or actual value (The difference in
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reading is known as the error).
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There are two types of errors, namely:
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Systematic errors results in the measurement or reading being consistently over the actual value
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OR consistently smaller than the actual value.
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Sources of systematic errors.
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Zero Error is caused if the reading shown is Not zero when the true value is
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actually zero. This is most probably caused by a flaw in the instrument for example when using a
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ruler that has lost its zero scale due to wear and tear hence causing an error in the measurement
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For example if you assume that water boils at 100 degree Celsius
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but actually its boiling point is higher if there are impurities in it. (Pure water boils at 100 degree
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For example in a sports day, when measuring a 100 m running
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time using a stopwatch. The observer may not press the stop button exactly when the foot of the
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runner touches the finishing line.
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Instruments that are not properly calibrated could also cause error
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and this has to be put in consideration when writing a report or when there is an anomaly in
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Random error is caused by the observer who reads the measuring instrument. Just like the
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systematic error, there is also positive or negative error. Positive error is when the reading is
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bigger than the real value and negative error is when the reading is smaller than the real value.
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Taking several readings and then find the average.
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Avoiding parallax error by positioning the instrument (meter rule) properly on the table
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with the eyes perpendicular to the scale.
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Some instruments can be adjusted to eliminate zero error. For example when using an
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ammeter, there is an adjuster to set the indicator to zero before making any measurement.
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In the case of a ruler, measurement can be carried out starting from the next clear scale
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for example if scale 0.0cm is blurred, we can start measuring the length fr om 2.0cm, of course
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taking the difference of value in consideration when recording the final reading.
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Density and Relative Density
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The Concept of Density of a Substance and its S.I Unit
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Explain the concept of density of a substance and its S.I unit
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of a substance is its mass per unit volume.
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The unit of density is kg/mˆ3. Other unit used is g/cmˆ3.Density of regular solid object can easily
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be found by direct and easy measurements.-It involves measuring the mass and calculating the
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volume as described in the experiment below.
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The Density of Regular and Irregular Solids
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Determine the density of regular and irregular solids
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Aim; To measure the density of rectangular block.
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Material and Apparatus :Ruler, beam balance and rectangular block.
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Procedures:Using a beam balance measure mass of the block, m.Measure its length, width and
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The mass of the rectangular block is m.
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The volume of the rectangular block will be calculated by multiplying the obtained
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length, l height, h and width, w.
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Volume, V = l x h x w, But; Density = mass/volume
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The volume of a material can be obtained by using various methods depending on the
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Aim; To determine density of irregular solid.
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Materials and apparatus:Irregular solid like stone, measuring cylinder, beam balance and water.
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Obtain the mass of the given object using the beam balance.
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Fill water to the measuring cylinder to the volume V
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Immerse the well tied irregular object totally in the cylinder containing water.
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Volume of irregular object = V
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Determine the density of a liquid
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Density of liquids can be determined by using a burrete or a density.
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Aim: To determine density of liquids using a burette.
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Materials and apparatus: Burette, beaker, beam balance and kerosene.
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Record the mass of the empty beaker m
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Pour the known volume of kerosene into the beaker by using bur rete, V.
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Record the mass of the beaker and kerosene m
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Definition of the Relative Density of a Substance
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Define the relative density of a substance
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of a substance is the ratio of its density to the density of water.The density
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of water has the density of approximately 1.0g/cm³ or 1000kg/m³.
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Since the density of pure water is 1g/cm³, the RD of a substance will be represented by the
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same number as its density in g/cm³.RD
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as its ratio of same quantities.
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Applications of Density and Relative Density in Real Life
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Interpret applications of density and relative density in real life
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Application of RD in real life
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It is the key factor which is considered during the design of various structures and
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equipment. Eg. ships and planes.
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Density is considered during the selection of materials.
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Density is also considered during the design of equipment used in swimming.
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