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Friday, 15 November 2019

Microprocessor Assignment Topics and Solutions

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Microprocessor Assignment Topics and Solutions

1. Assembler Instruction format, different programming models

An assembler is a software, which converts assembly language program codes to machine language. Assemblers are available in different types.

In one pass assembler, the source code is processed only once, and we can use only backward reference. In one pass assembler as the source code is processed, any labels encountered are given an address and stored in a table. Whenever a label is encountered, the assembler may look backward to find the address of the label.

In two pass assembler, the first pass is made through source code3 for the purpose of assigning an address to all the labels and to store this information in a symbol table. The second pass is made to actually translate the source code into machine code.

The interrupt for the assembler is the source program which is saved with file extension ‘ASM’. The assembler usually generates two output files called object file and list file. The object file consists of relocatable machine codes of the program and it is saved with file extension “OBJ”. The list file contains the assembly language statements, the binary codes for each instruction and address for each instruction. The list file is saved with file extension ‘LST’.

The list file also indicates any syntax errors in the source program. The assembler will not identify the logical errors in the source program. In order to correct the errors indicated on the list files, the user have to use the editor again. The corrected source program is saved again and then reassembled. Usually, it may take several times through edit – assemble loop to eliminate the syntax errors from the source program.

Some examples of assemblers are TASM (Borland’s Turbo Assembler), MASM (Microsoft’s Macro Assembler), ASM86 (INTEL’s 8086 Assembler) etc.

2. Assembly LINKER:

The liner is a software tool which is used to combine relocatable object files of program modules and library functions into a single executable file.

While developing a program for particular application, it is much more efficient to develop the program in modules. The entire task of the program can be divided into smaller task and procedures for each task can be developed individually. These procedures are called program modules. For certain task, we can use library files, if they are available. Each module can be individually assembled, tested and debugged. Then the object files of program modules and the library files can be linked to get executable file.

The linker also generates a link map file which contains the address information about the linked files. Some examples of linkers are microsoft’s linker LINK, Borland’s Turbo linker TLINK etc.

3. PROCEDURES AND MACROS:

When a group of instructions are to be used several times to perform a same fraction in a program, then we can write them as a separate subprogram called Procedure or Subroutine.

The procedures are written and assembled as separate program modules and stored in memory. When a procedure is called in the main program, the program control is transferred back to main program. In 8086 Processor, the instruction CALL is used to called a procedure in the main program and the instruction RET is used to return the control to main program.

A macro is a small group of instructions enclosed by the assembler directives MACRO and ENDM.

The macros are identified by their name and usually defined at the start of a program.
The macro is called by its name in the program, the assembler will insert the defined group of instructions in place of the call. In otherwords, the macro call is like Short hand expression which tells the assembler “Every time you see a macro name in the program, replace it with the group of instructions defined as Macros”.

Procedure
MACRO
1. Accessed by CALL and RET mechanism during execution.
1. Accessed during assembly with name given to macro when defined.
2. Machine code for instructions are stored in memory once.
2. Machine codes are generated for instructions in macro each time, it is called.
3. Parameters are passed in registers, memory locations or stack.
3. Parameters are passed as part of statement which calls Macro.

4. ASSEMBLER DIRECTIVES

Assembler Directive
Function
ASSUME
Indicates the name of each segment to the assembler.
BYTE
Indicates a byte sized operand
DB
Define byte. Used to define byte type variable.
DD
Define double word. Used to define 32 bit variable.
DQ
Define quad word. Used to define 64 bit variable.
DT
Define ten bytes. Used to define ten bytes of a variable.
DUP
Duplicate. Generate duplicates of characters or numbers.
DW
Define word. Used to define 16-bit variable.
END
Indicates the end of program.

Wednesday, 13 November 2019

Shaded Pole Motor Working Principle

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In this type of motor, the rotor is of squirrel cage and the stator salient pole type. A part of the pole is cut from the pole face and a copper ring is slipped into it as shown in Fig.

When the pole is excited by the field winding by a single phase supply, current flowing through the field winding produces an alternating flux. The part of the flux passing through the copper ring sinks with it inducing e.m.f. in the copper ring. Since the ring is a closed circuit like that of a coil, and due to induced e.m.f. in the ring, a current flows through the ring which in turn produces flux in the core. The direction of flux due to the current in the copper ring will oppose the main flux resulting in lagging of the flux with respect to the flux in the unshaded portion of the pole face.

Consider the flux produced in Fig. In Fig. (a) when the e.m.f. in the main pole rises from zero, e.rn.f. is induced in the ring which sets up large current. The flux produced by this current opposes the main flux and hence most of the flux shifts to the unshaded portion. In Fig. (b) when the e.m.f. in the main pole is maximum no e.m.f. is induced in the ring and the flux in the shaded and unshaded portion will be equal. The magnetic axis is shifted from the unshaded portion to the centre of the pole. In Fig (c) the e.m.f. in the main pole is decreasing from maximum value. It again induces e.m.f. in the ring.


The current in the ring produces flux which aid the flux in the shaded portion due to'which the flux is strengthened in the shaded portion. The magnetic axis is again shifted from the centre of the pole to the shaded portion of the pole face. The ,total effect correlates to the rotating magnetic field. A starting torque is developed and the rotor starts rotating in a fixed direction. The motor accelerates and runs at a speed lesser than the synchronous speed. The direction of rotation depends upon the position of the shading coil on the pole, since the rotation depends upon the position of the shading coil on the pole. Since the starting torque is less than the capacitor start motors, it is used in clocks, phonographs, instruments, hair dryers, small fans etc. Shaded pole motors are built commercially for small capacity varying from 1/250 h.p. to 1/6 h.p. These motors are simple in construction, rugged, reliable and cheap. The disadvantages in this type of motors are :-

a. it has low starting torque
b. it has very little overload capacity
c. its efficiency is low

A typical torque speed curve of shaded pole motor is shown in Fig.

Split Phase Motor

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SPLIT PHASE MOTOR

1. Capacitor Start Capacitor Run Motor :

In this type the stator is wound with two sets of a coils displaced by 900 electrical. The main or running winding has low resistance and high inductance and is connected across the supply. The starting or auxiliary winding is connected across the supply through a capacitor as shown in Fig. I f the capacitor is connected even while running then it is called capacitor start capacitor run motor and if during running it is cut off with the help of a centrifugal switch, it is called capacitor start induction run motor. Almost all ceiling fans are capacitor start capacitor run motors and most of the single phase pump are capacitor start induction run motors.

Since the running winding is inductive and the starting winding is capacitive, the two currents have a phase difference between them as shown in the vector diagram (See Figure). These two currents Is and lm produce a revolving flux as in the case of 3 phase induction motor due to which the torque produced in the rotor gives the direction. Hence the motor is self starting. Since the capacitor remains permanently in the circuit, motor, is sometimes referred as Permanent split capacitor run motor behaves practically like a unbalanced 2 phase motor. The capacitance usually used are 2 to 20 micro farads because of continuous duty rating which results in small starting torque of about 50 to 100 % of the rated value. Refer to Fig which gives the relation between percentage speed and percentage full load torque. These motors are used where starting torque is low such as fans, voltage regulators and oil burners. These motors are quite in operation and trouble free.


The advantage of keeping the capacitor continuously in the circuit are :

a. It improves the overload capacity of the motor
b. works on high power factor
c. has higher efficiency
d. runs smoothly

2. Capacitor Start Induction Run Motors :

In the capacitor start induction run motor, the capacitor serves short duty' service and gets cut-off when the motor reaches 73% of full load speed. For this purpose a centrifugal switch is incorporated in series with the starting winding. Usually electrolytic capacitors are used. In such type the main winding is designed to carry WI load current. Fig shows the connection diagram of a capacitor start induction run motor which uses a switch for disconnecting the capacitor from the circuit while Fig (b) shows the diagram of the centrifugal switch.
The necessary phase difference between the two torques lire and Is is provided by connecting a capacitor in series with the starting winding. The capacitor is so designed that it is capable of operating 20 operations per hour not exceed 3 seconds per operation. The phasor diagram of the currents is shown in Fig.

The current due to the main winding lags the voltage V by a large angle whereas the current due to starting winding leads the V by certain angle. Thus the phase difference between the two currents is large of about 80o thus increasing the value of torque produced.

TYPES OF CAPACITOR START MOTORS

Some important types of capacitor start motors which are manufactured are dealt below.

1. Single Voltage External Reversible Type:

In this type of motor, four leads are brought out, two from each of the main and Starting winding. The starting winding is connected in series with the electrolyte capacitor and a centrifugal switch and for reversing the direction of rotation, the leads of the starting winding is reversed with respect to the running winding with the help of a switch.

2. Single Voltage Non-Reversible with Thermostat :

Thermostat provides protection against overload and short circuits. When overload occurs, the bi-metallic contacts of the thermostat opens and thus disconnects the motor from the supply. The contacts gets reconnect again when the bi-metal cools.

3. Single Voltage Non Reversible with Magnetic Switch :

Where the use of centrifugal switch is not possible, and if direction of rotation is required, a plunger type magnetic switch is used.

4. Two Voltage Non Reversible Type:

These motors are designed to operate on two voltages such as 110V and 220V . Two main windings are provided separately or one main winding in two sections are provided. One starting winding with suitable number of leads are brought out to permit change over from one voltage to another. When the motor is to operate from lower voltage, the two main windings are connected in parallel and for higher voltage, the main windings are connected in series.

5. Two Voltage Reversible Type :

In this type, two additional leads are brought out from the starting winding for reversing the direction of rotation externally.

Tuesday, 12 November 2019

Single Phase Induction Motor Working Principle

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INDUCTION MOTOR

INTRODUCTION

In general the construction of single phase motors is similar to a three phase squirrel cage induction motor except for the stator winding. The stator contains a set of windings producing several pairs of poles. When connected to an alternating current supply, the polarity of these poles would alternatively become north and south due to which a pulsating torque is produced locking the rotor stationary i.e., the torque produced will try to rotate the rotor in both the direction.

If the rotor is given a push in any direction, it would pick up speed and continue to run in the same direction. Hence, a single phase motor is not self starting. The auxiliary methods used are splitting the single phase into two phases or shading the pole to obtain a directional torque.


WORKING PRINCIPLE OF OPERATION OF A SINGLE PHASE INDUCTION MOTOR

The peculiar behavior of the single phase motor can be explained into two ways :

(a) by cross field theory
(b) double field revolving theory

To overcome the problem and to make the single phase induction motor self starting it has to be feed in either from 2 phase or three phase supply the field produced by the supply may be made to revolve for producing self starting capability.

Cross-Field Theory : Consider a single phase induction motor having 1-Φ winding on stator and squirrel-cage rotor.

Assume that the rotor is now given an initial rotation in the clockwise direction. An e.m.f. called rotational e.m.f is induced in the rotor winding due to the stationary stator field. The direction of induced e.m.f. in the rotor conductors is shown in Fig. E.M.F. induced in the rotor conductors is in one direction on one side of the vertical axis and in the opposite direction on the other side of the vertical axis.

As the rotor circuit is closed the voltage so induced will produce a rotor current and a rotor e.m.f. wave whose axis is displaced by 90 degrees electrical from the stator axis. The frequency of the rotor-induced e.m.f. is high and, therefore, the rotor reactance is also high. The rotor current will lag the rotor induced e.m.f. by about 90 degrees. The field produced by rotor current, Φr known as cross-field will have a time-phase difference of 90 degrees with the stator field Φσ. Tηvσ the stator flux (Φs), and rotor flux Φr are in space time quadrature. These two fields will produce a revolving field (as in 2-phase supply) which will rotate in the direction in which the rotor was given an initial rotation. Thus the torque produced will be in the same direction as that of rotation.

Double Revolving Field Theory :

This theory is based on the fact that the alternating flux produced by stator winding can De represented as the sum of two oppositely-rotating vectors of half-magnitude. The summation of the vectors is a vector that changes in length along the horizontal axis.

Let Φm = maximum value of the alternating flux
A = B = Φm/2 component fluxes of Φs, revolving in clockwise, anti-clockwise respectively.
Φr = stator resultant flux at any instant.

From fig, (a) it can be seen that the magnitudes of Φr at intervals of 0o, 45o, 90o, 135o and 180o are respectively equal to 0, 0.707 Φm , Φm , 0.707 Φm and 0. At θ = 0o, the two component fluxes A and B are shown in opposite directions. After a time interval of 45 degrees, A and B have rotated in clockwise and anti-clockwise directions respectively, Fig (c). At the interval of one-fourth cycle i.e., 90 degrees, Φr is maximum Fig (d). At q = 135°, fluxes A and B will have a resultant of 0.7074 Φm, Fig. (e). After half cycle, again the resultant flux is zero as shown in Fig (f) and so on. If the component vectors A and B are drawn for one cycle. It will be observed that each of the component flux vectors will rotate by one revolution.

Torques developed by two components A and B are acting in opposite directions, each component develops a torque that tends to rotate the rotor in the direction in which the field rotates. The resultant torque is the summation of the torques produced by the two components A and B as shown in Fig. It may be noted that torque-speed curve is drawn for a speed range of— Ns to + Ns. From the resultant torque-speed curve the following can be observed.

a. Average torque at standstill is zero, and therefore, the motor is not self-starting (at Ni = 0, torque developed by the A and B components cancel each other).

b. When rotor is given an initial rotation in any direction, the average torque developed causes the rotor to continue to rotate in the direction in which it is rotated initially.

Brief description of two theories has been given to explain why a single-phase induction motor will continue to rotate in a direction in which the rotor is given some initial rotation. To make the motor self-starting, some starting device or method has to be employed. Single-phase induction motors are named according to the starting methods employed.

Wednesday, 6 November 2019

Plastic Capacitor Construction

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PLASTIC CAPACITORS:

Plastic Capacitors is defined as those capacitors which uses plastic film as a dielectric. The different plastics that are used are Teflon, Polystyrene, Polyethylene and Polyester. When sealed properly these plastics exhibit good mechanical strength, resistance to heat and chemical inertness. These have high insulation resistance and low dielectric absorption. The Construction of different plastic capacitor are explained below.

Teflon :

Polytetrafluoro ethylene also known as Teflon is a heat resistance material. A thin films of Teflon are produced by dispersing a thin colloidal solution of Teflon over a metal surface. The film is removed after drying and heating the metal. In another method a metal strip is made to pass through liquid polytetrafluoro ethylene. The coating is, heated and then removed.


A thin film of aluminium is coated onto this by vacuum evaporation. This metalized film with plain film of Teflon is rolled to form a capacitor. Teflon can operate at higher temperatures and has better temperature coefficient. Insulation resistance is high and power factor is low.

Polystyrene :

These capacitors are made by rolling the polystyrene film with aluminium foil. These are compactly wound and the leads are welded at the ends. The entire assembly is heat treated so that the plastic softens and makes good contact with the metal foil. The winding requires particular attention because it may accumulate electrostatic charges and attracts dust. Polystyrene capacitors have a low power factor and cannot be used at temperatures beyond 65°C. It has high insulation resistance and good stability. It has the disadvantage that the capacitance decreases with temperature.

Polyester :

These are made of polyesters like Mylar, Melinex, Terelyne etc. also called as polyethylene terephthalate. This is usually metallised to give better results. Sometimes impregnation is done with silicons or mineral oil to improve the dielectric, characteristics. A thin film of silver is deposited on this plastic by vacuum evaporation. These capacitors are capable of withstanding temperatures upto 150°C and voltage upto 400 volts. These capacitors are available in the ranges of 100 pF to 2 μF. These capacitors have the disadvantages that dielectric constant increase with temperature and decreases with frequency. Since the dielectric is prone to moisture, good encasing is needed. The capacitors are usually encased in glass or ceramic containers; resin moulded or in jackets of silicon treated polystyrene.

These capacitors are preferred to those of paper capacitors. They have excellent high frequency characteristics and can be used at frequencies of 40 MHz. Insulation resistance is high. The disadvantages are that the power factor varies with the temperature. The capacitance also increases with increase in temperature. The dielectric absorption is high and can withstand voltages upto 250 volts.

Polycarbonate :

The metallised polycarbonate film is rolled and hermetically sealed in a metal case with epoxy resin. It is insulated with a polyester sleeve. Because of its protection from moisture it provides stable capacitances with a high temperature coefficient. It has very high insulation resistance but can be operated only upto 85°C. They are not capable of withstanding high voltages. These are available in the ranges 0.1 to 10 μF.

Monday, 4 November 2019

Types and Uses of Electrolytic Capacitors

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Types and Uses of Electrolytic Capacitors

These capacitors have low volume for large capacitance especially at low working voltages and can be used for high energy pulse storage application. Electrolytic capacitors are for direct voltage working. Different types of electrolytic capacitors are dealt in succeeding paragraphs.

Aluminium Electrolytic Capacitor :

Aluminium oxide which is formed by a process of electrolysis on an aluminium electrode acts as dielectric in these capacitors. During the process of manufacture, the electrode is connected to positive of voltage source and is therefore called anode. Aluminium borate solution is used in the production of oxide film. The film is thin and therefore has high capacitance per unit space occupied by capacitor. The electrolyte in contact with aluminium anode, oxide coating behaves as the other electrode of the capacitor. The second coating behaves as the other electrode of the capacitor. The second terminal is connected to the non oxide aluminium foil. In the rolled electrolyte capacitor the anode consists of a long strip aluminium foil carrying the oxide film on both sides. Aluminium borate electrolyte solution is held in an absorbent paper tissue strip of similar length. A second strip of aluminium foil with no oxide film lies next to paper tissue and acts as the cathode. The three strips are rolled tightly and outer cover of aluminium is provided.


These capacitors are available in polarised or non-polarised form. In polarised type the oxide film is formed on the positive electrode only and the negative electrode is used only for connections. In the non-polarised form two polarised capacitors are to be connected back to back or by using both the electrodes with oxide films. Polarised capacitors are to be connected only in one direction. A change in polarity of connection allows the capacitor to draw high currents and gets heated. Such capacitors are used as filters for power supply. The non polarised form used in series with the starting winding of capacitor start inductions run motor and in the case of ceiling fan.

In some capacitors a solution of Boric Acid ammonium metaborate and glycol is used as electrolyte. The foil with the oxide film on both sides acts as the anode and an ordinary foil acts as cathode. These are rolled with kraft paper separations and encased in an aluminium casing and leads taken out. It has a polarity marking on it.

In the electrolyte capacitors since the oxide film is not a perfect insulator high leakage current will result and is of the order of 0.1 to 0.5 mA per Farad of capacitance and working temperature is limited to 80°C. The power factor of these capacitors is ten times the paper capacitor and is mainly due to the resistance film. The power may decrease with temperature and increases with frequency. The polarised capacitors are used as coupling capacitors in RC amplifier, as bias and decoupling capacitors, filters in rectifier circuits.

Tantalum Electrolytic Capacitors :

In the new type of electrolytic capacitors tantalum or Niobium is used. The dielectric oxide film Tantalum Pentoxide can be electrolytically formed on tantalum. This has higher dielectric constant and more stable than aluminium oxide. In the wet type electrolytic capacitor, the electrolytes used are sulphuric acid or lithium chloride or Boric Acid and in the solid type manganese dioxide is used.

Wet Type Tantalum Capacitors : 

In this type the anode is capsule shaped and is made of compressed powder of Tantalum and sintered in vacuum at 2000°C. An oxide layer is formed electrolytically. The cathode is cup shaped and made of silver. It contains a liquid electrolyte of very high conductivity. Lithium chloride is used as electrolyte. The anode is immersed in electrolyte and the cup sealed with a plate. The anode and cathode are separated by Teflon seal.
Tantalum Electrolytic Capacitors
Solid Type Electrolytic Capacitors :

In this type of tantalum powder is pressed to form a pellet in a die set and sintered at controlled temperature of 2000°C by which high bonding strength is acquired. The size of granules of tantalum powder determines the capacitance value. The pellet is then inserted in maganese sintrate. Decomposition from nitrate to oxide takes place and manganese oxide is formed. Graphite is then coated on the oxide layer and a copper coil or metal sprayed is covered. Lead wires are taken out and the entire assembly is encased in moulded tubular or rectangular plastic case with resin seal.

These are low voltage capacitors with a working temperature of 100°C. It has good ripple voltage rating and has low leakage due to high conductivity of manganese oxide layer.

Some of the features are :

(a) Its cost per microfarads is very low.
(b) Leakage current is less than wet type.
(c) Series resistance is less than wet type.
(d) Polarised and non polarised are available.
(e) The voltage ranges from 25V to 500 volts.
(f) The power factor is low and increases with frequency and applied voltages.

Uses of Electrolytic Capacitors :

Electrolytic capacitors are used in circuits that have a combination of de voltage and ac voltage. The dc voltage maintains the polarity. They are used as ripple filters where large capacitances are required at low cost in small space. They are also used as bias capacitors and decoupling capacitors. They are used as coupling capacitors in R-C amplifier stages.

Sunday, 3 November 2019

Measurements in Chemistry Notes

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Measurements in Chemistry Notes:

Chemistry is basically an experimental science, which involves measurements of physical quantities of the phenomenon under observation. Every measurement is made relative to some reference standard known as the unit of the measurement. A unit is defined as the standard of reference chosen to measure any physical quantity.

For example, the measured length of a pencil is 8.6 cm means that the length of the pencil is 8.6 times the unit of measurement, which is one cm in this case. Thus the result of any measurement is a combination of a pure number and a unit (8.6 cm here).
Significant Figures:

measurement involving only counting (the discrete variable) like the number of students in a class, number of pens in a box, etc. does not have any uncertainty. They are exact numbers.

However, every measurement, which is made by some instruments (continuous variable) like the height of a boy measured with a tape, volume of water in a beaker measured with a burette, etc. is associated with some degree of uncertainty. The extent of uncertainty depends on the accuracy of the measuring device and the skill of the operator. when the result of such a measurement is expressed it should indicate the degree of uncertainty involved. This is done in terms of significant figures. It indicates the precision of the measured quantity.

The total number of digits in a number is called the number of significant figures. the significant numbers in a number are the number of digits are certain plus one that is uncertain, beginning with the first non-zero digit. The greater the number of significant figures, the greater is the precision. For example, the volume of water in a beaker measured by using a measuring cylinder and the by using a burette, has been reported as 160 cm3 and 160.0 cm3. The number of significant figures in these cases are three and four respectively. This implies that in the first volume (160 cm3) the digits 1 and 6 are certain and the third digit 0 is uncertain. The precision of the apparatus is 1 cm3. Therefore the true value lies between 159 and 161 cm3. But in the second volume, (160.0 cm3) the digits 1,6 and 0 are certain and only the last digit 0 is uncertain. Here the precision is 0.1 cm3. Therefore the true volume lies between 159.9 cm3 and 160.1 cm3. The second measurement is more precise in these cases.



Rules for determining Significant Figures in a number
The following rules are observed to determine the number of significant figures in a number.

1. All non zero digits as well as the zeros between the non-zero digits are significant. For example, 168 cm has three significant figures and the number 180045 has six significant figures.

2. When the numbers start with a decimal, zeros to the left of the first non zero digit are not significant. Thus 0.5412, 0.05412, 0.005412, all have four significant figures. However zeros to the right of the first non-zero digits are significant. For example, 0.50, 0.050, 0.500 and 0.5100 have two, two, three and four significant figures respectively.

3. If a number has an integral part and a decimal part, all zeros in the number are significant. For example, 7.05, 75.10, 75.050 have three, four and five significant figures respectively.

4. When there is no decimal point in a number, the last zeros may or may not be significant. For example, 20200 g may have three, four or five significant figures depending upon the precision.

In such cases expressing the numbers in scientific notation helps to remove the ambiguity regarding the number of significant figures. in scientific notation, the number is written in the standard exponential form as N x 10n, where N is a number with a single non-zero digit to the left of the decimal point, and n is an integer. In exponential notation, the numeric portion indicates the number of significant  figures. For example, the above mass may be written as 2.02 x 104 g which has three significant figures. But if it is precise to four or five significant figures, then the number should be written as 2.020 x 104 g and 2.0200 x 104 g respectively. Thus Avogadro's constant 6.023 x 1023 mol- 1 and Planck's constant 6.62 x 10-34 Js have four and three significant figures respectively.

Example :

Express the following in scientific notations (a) 8614 (b) 0.00178

(a) 8.614 x 103
(b) 1.78 x 10-3

Example :

Find the significant figures in each of the following

(a) 0 0656 g     (b) 451 cm3            (c) 4.0062
(d) 0.070         (e) 6.02 x 1023         (f) 3.50 x 103g

Answers          (a) 3    (b) 3     (c) 5      (d) 2       (e) 3     (f)  3

Computation Rules:

To compute the final result of an experiment, mathematical manipulations such as addition, subtraction, multiplication and division are required. When several numbers of varying precisions are computed (added, subtracted, multiplied, or divided) the final answer cannot be more precise than the least precise number involved in the computation. Following rules are used for the purpose of determining the number of significant figures in the results.


Rounding off the results

I While reporting the results, the last digits may be rounded off, if required, to avoid figures that are not significant.

2 All digits to be rounded off are removed together (however, rounding is done separately for mixed calculations involving addition-subtraction, and multiplication-division).

3. If the digit following the last digit to be retained is less than 5, the last digit is left unchanged. However, if the digit is greater than 5, the last digit to be retained is increased by one.

4. If the left most digit to be removed is 5, the last digit retained is not altered if it is even but increased by one if it is odd.  

Example :

Round off the number 58.69536 to three significant figures.

Answer:  The number is rounded off to three significant figures as 58.7 because the number to be dropped (9) is greater than 5.

Example :

Round off the following numbers 57.250 and 57.350 to three significant .figures.

Answer:   57.250 is rounded off as 57.2; 57.350 is rounded off as 57.4
In addition and subtraction, the result should be reported to the same number of decimal places as that of the term with the least number of decimal places.

Example:

(a)        Addition         24.2               14.3042             154.2
                                    2.22               3.0258               6.1
                                    0.222             0.0016               23

Actual value =             26.642            17.3316          183.3
Reported value            26.6                17.3316          183

(b)        Subtraction      5.2848                        13.64               26.382
                                    -5.2822                       -0.0016           -8.4593

Actual value =            0.0026                       13.6384          17.9227
Reported value =        0.0026                        13.64              17.923

The answers in the case of (a) are reported to

(1) one decimal place
(2) four decimal places
(3) nearest whole number

The answers in the case of (b) are reported to

(1) same decimal places
(2) two decimal places
(3) three decimal places.

In multiplication and division, the result should be reported to the same number of significant figures as the least precise term in the computation.

 Example :   (a) 50.122 x 1.21 = 60.6;
                     (b) 0.364 ÷ 4.974 = 0.072

The presence of exact numbers in an expression does not affect the
number of significant figures in the answer.

Example :
Here '3' is an exact number and the answer is reported to 3 significant figures.

SI Units:

In order to have consistency in the scientific recording, IUPAC has recommended the use of international system of units. It is popularly known as the SI units (after the French expression System Internationally).

The SI has seven basic units which are dimensionally independent. All other units are derived from these basic units.

The Seven basic SI Units:

Name of Unit
Physical Quantity
Symbol
Metre
Length
m
Kilogram
Mass
kg
Second
Time
s (sec)
Ampere
Electric Current
A
Kelvin
Temperature
K
Candela
Light Density
cd
Mole
Amount of Substance
mol

Some common SI Derived Units:

Physical Quantity

Name of Unit
Symbol for Unit
Definition in SI Basic Units
Area
---
---
m2
Volume
---
---
m3
Density
---
---
kg/ m3 or kgm-3
Speed
---
---
m/s or m s-1
Acceleration
---
---
m/s2 or m s-2
Force
Newton
N
Kg m s-2
Pressure
Pascal
Pa
Kg m-1 s-2 or Nm-2
Energy
Joule
J
Kg m2 s-2
Power
Watt
W
Kg m2 s-3  or  J s-1
Frequency
Hertz
Hz
s-1
Electric Charge
Coulomb
C
A s
Electric P. D.
Volt
V
JA-1s-1     or
kg m2 s-3 A-1

 The standard prefixes for expressing the decimal Fraction or Multiples of Fundamental Units:

Prefix
Symbol
Multiple

exa
E
1018
peta
P
1015
tera
T
1012
giga
O
109
mega
M
106
kilo
k
103
hecto
h
102
deca
da
10
deci
d
10-1
centi
c
10-2
milli
m
10-3
micro
μ
10-6
nano
n
10-9
pico
p
10-12
femto
f
10-15
atto
a
10-18

Dimensional Analysis

Any calculation involving the use of the dimensions of physical quantities is called dimensional analysisIt is used as a problem solving technique. For example, lets consider the conversion of 3 weeks into days.

1 week = 7 days;
The above equations are called the unit conversion factor. Since the two ratios given above are equal to unity, the multiplication or division of a physical quantity by these factors does not change the value of the quantity but changes the units in which the quantity is expressed. thus to convert 3 weeks into days. 
The correct conversion factor must be used for a particular conversion. The numerator of the conversion factor must be the desired unit and the denominator must be the original unit.

Example :

Let's find out how many minutes are there in 7 days

Answer:
Example:

Calculate the mass of a box in kg which weights 100 lb.

Answer:
It is also used as a very powerful tool to check the correctness of equations. In an equation, the dimensions of all the terms on either side are the same.

For example, in the equation

PV = nRT,  the dimensions are
mass  x  length2  x  time-2 on both sides.