Notes

Science:

The knowledge gained through observations and experiments is called Science. The word science is derived from the Latin word Scientia, which means knowledge. Not until the eighteenth century, various aspects of material objects were studied under a single subject called natural philosophy.

Division of science:

As knowledge increased, it was divided into two main streams.

1. Physical sciences:

    Physical sciences - deal with the study of non-living things.

2. Biological: sciences:

    Biological sciences - are concerned with the study of living things.

Physics:

           Physics is that branch of science that deals with the study of properties of matter-energy and their mutual relationship.

Branches of physics:

1. Mechanics; It is the study of the motion of objects, their causes, and their effects.

2. Heat: Deals with the nature of heat modes of transfer and effects of heat.

3. Sound: It deals with, the physical aspects of sound waves, their production, properties, and applications

4. Light (Optics): It is the study of physical aspects of light, its properties, working, and use of optical instruments.

5. Electricity and Magnetism: It is the study of the charges at rest and in motion, their effects, and their relationship with magnetism.

6. Atomic Physics: It is the study of the structure and properties of atoms.

7. Nuclear Physics: It deals with the properties and behavior of nuclei and the particles within the nuclei.

8. Plasma Physics: It is the study of production, and properties of the ionic state of matter - the fourth state of matter.

9. Geophysics: It is the study of the internal structure of the Earth.

Kelvin statement:

When you can measure what you are speaking about and express it in numbers, you know something about it. When you cannot measure what you are speaking about or you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind.

 

FOR YOUR INFORMATION

Andromeda:

                Andromeda is one of the billions of galaxies in the known universe.

The crucial role of physics in science, technology, and society:

 The rapid progress in science during recent years has become possible due to the discoveries and inventions in the field of Physics. The technologies are the applications of scientific principles. Most of the technologies of our modern ° society throughout the world are related to Physics.

Examples:

1. A car is made on the principles of mechanics and a refrigerator is based on the principles of thermodynamics.
2. Consider pulleys that make it easy to lift heavy loads.
3. Electricity is used not only to get light and heat but also mechanical energy that drives fans and electric motors etc.
4. Consider the means of transportation such as cars and airplanes; domestic appliances such as air-conditioners, refrigerators, vacuum cleaners, washing, machines, microwave ovens, etc.
5. Similarly, the means of communication such as radio, TV, telephone, and computer are the result of applications of Physics. These devices have made out lives much easier, faster, and more comfortable than in the past.
6. A mobile phone allows us to contact people anywhere in the world and to get the latest worldwide information. We can take and save pictures, and send and receive messages from our friends. We can also receive radio transmission and can use it as an e calculator as well.

Scientific inventions have also caused harm and destruction of serious nature. One of which is the environmental pollution and the other is the deadly weapons.

DO YOU KNOW?

Wind turbines are used to produce pollution-free electricity.

Quick Quiz

1. Why do we study physics?

Ans:   We study physics because Physics is the branch of science that deals with matter, energy, and their interaction. Most of the technologies of our modern society throughout the world are related to physics.

 

2. Name any five branches of physics?

 Ans: 

1. Thermodynamics
2. Electromagnetism
3. Atomic Physics
4. Plasma Physics
5. Mechanics

 

Physical Quantities:

All measurable quantities are called physical quantities such as length, mass, time, and temperature.

A physical quantity possesses at least two characteristics in common. One is its numerical magnitude and the other is the unit in which it is measured.

Examples:

For example, if the length of a student is 104 cm then 104 is its numerical magnitude and a centimeter is the unit of measurement.

Similarly, when a grocer says that each bag contains 5 kg of sugar, he is describing its numerical magnitude as well as the unit of measurement. It would be meaningless to state 5 or kg only.

Physical quantities are divided into base quantities and derived quantities.

 

Difference between base quantities and derived quantities:                                                                    

1. Base quantities:

             Base quantities are the quantities based on which other quantities are expressed.

Seven physical quantities form the foundation for other physical quantities. These physical quantities are called the base quantities.

Example:

Length, mass, line, electric current, temperature, the intensity of light, and the derived quantities.

 

2. Derived quantities:

             The quantities that are expressed in terms of base quantities are called derived quantities.

Example:

Area, volume, speed, force, work, energy, power, electric charge, electric potential, etc.

Unit:

Once a standard is set for a quantity then it can be expressed in terms of that standard quantity. This standard quantity is called a unit.

An international system of units:

The eleventh General Conference on Weight and Measures held in Paris in 1960 adopted a worldwide system of measurements called the International System of Units. The International System of Units is commonly referred to as SI.

Base units:

The units that describe base quantities are called base units. Each base quantity has its SI unit. The table shows seven base quantities, their SI units, and their symbols.

 

Base quantities, their SI units with symbols quantity Unit Name Symbols

Quantity		Unit
Name	Symbol	Name	Symbol
Length	|	meter	m
Mass	M	kilogram	kg
Time	T	second	s
Electric current	I	ampere	A
Intensity of light	L	candela	cd
Temperature	T	kelvin	K
Amount of a substance	N	mole	mol

1. SI system is in use all over the world.

2. Manipulation in this system is quite easy i.e. the multiple and sub multiple of different units is obtained simply by multiplying or dividing with ten or powers of tens.

Derived units:

          The units used to measure derived quantities are called derived units.

Derived units are defined in terms of base units and are obtained by multiplying or dividing one, or more base units from each other.

 Examples:

1. The unit of area (meter)² and the unit of volume (meter)³ are based on the unit of length, which is meter. Thus, the unit of length is the base unit while the unit of area and volume are derived units.
2. Speed is defined as the distance covered in unit time; therefore, its unit is a meter per second. In the same way, the unit of density, force, pressure, power, etc. can be derived using one or more base units.

 

Derived quantities and their SI units with symbols

Quantity		Unit
Name	Symbol	Name	Symbol
Speed	V	meter per second	ms-1
Acceleration	A	meter per second per second	ms-2
Volume	V	cubic meter	m3
Force	F	newton	N or (kg m s2)
Pressure	P	pascal	Pa or (N m-2)
Density	Ρ	kilogram per cubic meter	Kgm-3
Charge	Q	coulomb	C or (As)

Quick Quiz

 

1. How can you differentiate between the base and derived quantities?

 Ans: Difference between the base and derived quantities:

Base Quantities	Derived Quantities
i.    Base quantities are the quantities based on which other quantities are expressed.	i. The quantities that are expressed in terms of base quantities are called derived quantities
ii. Length, mass, time, electric current, temperature, the intensity of light | and the amount of a substance.	ii. Area, volume, speed, force, work, energy, power, electric charge, electric potential, etc.

2. Identify the base quantity is the following:

1. Speed 2. Area 3. Force  4. Distance

The distance can be considered as a base quantity because the distance is equal to the length and its unit is a meter.

1. Speed, area, and force are derived quantities because these quantities are expressed in terms of base quantities.
2. Identify the following as base or derived quantity: density, force, mass, speed, time, length, temperature, and volume.

   Base Quantities	Derived Quantities
   Length, mass, time, temperature.	Density, volume, speed, force,

    

              Ans

   

   Mini Exercise

   Volume is a derived quantity

   1L        = 1000mL

    1L       = 1 dm³

               = (10cm) ³

               = 1000 cm³

    1mL = 1 cm³

    Express 1 m³ in liters    ......... L

   Solution: -1m³ in liters=1000L

Prefixes:

          Prefixes are the words or letters added before Si units such as kilo, mega, giga and milli.

         SI units have the advantage that their multiples and sub-multiples can be expressed in terms of prefixes. These prefixes are given in Table.

                                                             Some Prefixes

Prefix	Symbol	Multiplier
exa	E	1018
peta	P	1015
tera	T	1012
giga	G	109
mega	M	106
Kilo	K	103
hecto	h	102
deca	da	101
deci	d	10-1
centi	c	10-2
milli	m	10-3
micro	M	10-6
nano	n	10-9
Pico	P	10-12
femto	f	10-15
atto	a	10-18

Advantages of prefixes:

       The prefixes are useful to express very large or small quantities. For example, divide 20,000 g by 1000 to express it into kilogram, since kilo represents 10³ or 1000.

Thus 20,000g = 20,000 ÷ 1,000Kg  = 20kg

or    20,000 g     = 20 x 10g             = 20kg

Note:

Double prefixes are not used. For example, no prefix is used with kilogram since it already contains the prefix kilo.

           Prefixes given in Table are used with both types of base and derived units.

Multiples and sub-multiples of length:

1km	103m
1cm	102m
1mm	10-3m
1µm	10-6m
1nm	10-9m

Scientific notation/Standard form:

               In scientific notation, a number is expressed as some power of ten multiplied by a number between 1 and 10.

 Examples:

3. The Moon is 384000000 meters away from the Earth. The distance of the moon from the Earth can also be expressed as 3.84 x 10⁸ This saves writing down or interpreting large numbers of zeros.
4. A number 62750 can be expressed as 6.275 x 10⁴. Similarly, the standard form of 0.00045 is 4.5 x 10^-4

   Quick Quiz

1. Name five prefixes most commonly used.

Ans:     (1) kilo (k) = 10³      (2) centi(c)10^-2        (3) milli(m) = 10^-3

            (4) micro (u) = 10^-6        (5) mega (M) = 10⁶

 

2.The Sun is one hundred and fifty million kilometres away from the Earth. Write this.

(a) as an ordinary whole number

(b) In scientific notation.

 

Ans:    The distance of Sun from the Earth = 150 million km         

(A) as an ordinary whole number:

           = 150 x 10⁶km= 150 x 10⁶ x 10³m                                         1 million 10⁶ 1 kilo = 10³

                = 150000000000 m

(B) In scientific notation.

= 150 x 10⁶ x 10³

= 150 x 10⁹

 = 15 x 10 x 10⁹

= 15 x 10¹⁰

 

= 15 ÷ 10 x 10 x 10¹⁰

=1.5 x 10¹¹

=1.5 x 10¹¹ m

 

3. Write the numbers given below in scientific notation.

1. 3000000000 ms^-1 C.6400000 m
2. 0000000016 g       D. 0.0000548 s

Ans:

A. 3000000000 ms-1

= 3 x 1000000000 ms^-1

= 3x 10⁹ ms^-1 

 

B. 6400000 m

= 64 x 10⁵m

= 6.4 x 10 x 10⁵

= 6.4 x 10⁶m

 

C. 0000000016 g

= 0.0000000016 ÷ 10000000000 g

= 16 x 10^-10g

            =1.6x 10x 10^-10g

           =1.6x10^-9g

 

D. 0.0000548 s

 = 0.0000548

=    0.0000548 ÷10000000

=    548 x 10^-7

= 5.48 x 10² x 10^-7

=5.48x 10^-5 s 

 

Tidbits

 

FOR YOUR INFORMATION

Hubble Space Telescope:

                   Hubble Space Telescope orbits around the Earth. It provides information about stars.

The meter rule:

 

 

A meter rule is a length measuring instrument as shown in the figure. It is commonly used in laboratories to measure the length of an object or the distance between two points. It is one meter long which is equal to 100 centimeters. Each centimeter (cm) is divided into 10 small divisions called millimeters (mm). Thus, one millimeter is the smallest reading that can be taken using a meter rule and is called its least count.

Least count of meter rule = 0.1 cm or 1mm

The measuring tape:

 Measuring tapes are used to measure the length in meters and centimeters. A measuring tape used by blacksmiths and carpenters. A measuring tape consists of a thin and long strip of cotton, metal, or plastic generally 10 m, 20 m, 50 m, or 100 m long. Measuring tapes are marked in centimeters as well as in inches.

The least count of measuring tape = 0.1 cm or 1 mm

Mini Exercise

Cut a strip of a paper sheet. Fold it along its length. Now mark centimeters and half a centimeters along its length using a ruler. Answer the following questions:

1. What is the range of your paper scale?

Ans: The range of the paper scale is 20 cm.

 

2. What is its least count?

Ans: The least count of paper scale is 1 cm.

 

3. Measure the length of a pencil using you. Paper scale and with a meter ruler. Which one is more accurate and why?

Ans: The measurement of pencil measured by the meter ruler is 4.2 cm. The measurement of a pencil measured by the ruler is more accurate because it even can measure the length in millimeters.

Vernier calipers:

An instrument used to measure small lengths such as internal or external diameter or Length of a cylinder etc. is called Vernier Calipers.

 

 Construction:

              A Vernier Calipers consists of two jaws. One is a fixed jaw with the main scale attached to it.

 

Main scale:

          The main scale has centimeter and millimeter marks on it. The other jaw is moveable.

 

Vernier scale:

It has a Vernier scale having 10 divisions over it such that each of its divisions is 0.9 mm.

 

Least count (LC)/Vernier constant:

 The difference between one small division on the main scale division and one Vernier scale division is 0.1 mm. It is called the least count (LC) of the Vernier Calipers. The least count of the Vernier Calipers can also be found as given below:

Least count of Vernier Calipers = smallest reading on main scale ÷number of divisions on Vernier scale

                                                  = 1mm ÷ 10 divisions

   Hence                                   LC=0.1mm= 0.01 cm

 

Working of a Vernier Calipers:

First of all, find the error, if any, in the measuring instrument. It is called the zero error of the instrument. Knowing the zero error, necessary corrections can be made to find the correct measurement. Such a correction is called the zero correction of the instrument. Zero correction is the negative of zero error.

 

Taking a Reading on Vernier Calipers:

 Let us find the diameter of a solid cylinder using Vernier Calipers. Place the solid cylinder between the jaws of the Vernier Calipers. Close the jaws till they press the opposite sides of the object gently.

Note the complete divisions of the main scale past the Vernier scale zero in a tabular form. Next, find the Vernier scale division that is coinciding with any division on the main scale. Multiply it by feast count of Vernier Calipers and add it to the main scale reading. This is equal to the diameter of the solid cylinder. Add zero correction (Z.C) to get the correct measurement. Repeat the above procedure and record at least three observations with the solid cylinder displaced or rotated each time.

 

Zero Error and Zero Correction:

 To find the zero error, close the jaws of Vernier Calipers gently. If the zero line of the Vernier scale coincides with the zero of the main scale then the zero error is zero. Zero error will exist if zero lines of the Vernier scale is not coinciding with the zero of the main scale.

Positive zero error:

Zero error will be positive if the zero lines of the Vernier scale are on the right side of the zero of the main scale. | To get the correct value zero error must be recorded and subtracted from each reading.

 Negative zero error:

Zero error will be negative if the zero lines of the Vernier scale are on the left side of zero of the main scale.

To get the correct value zero error must be recorded and added to each reading.

 

Quick Quiz

 

1. What is the least count of the Vernier Calipers?

Ans: The least count of the Vernier Caliper is 0.1 mm or 0.01 cm.

 

2. What is the range of the Vernier Calipers used in your Physics laboratory?

Ans: The range of the Vernier Calipers used in your Physics laboratory is 12 cm.

 

3. How many divisions are there on its Vernier scale?

Ans: Vernier scale has 10 divisions over it such that each of its divisions is 0.9 mm.

 

4. Why do we use zero correction?

Ans: Zero correction is used to get a correct and exact measurement.

 

DIGITAL VERNIER CALLIPERS

Digital Vernier Calipers have greater precision than mechanical Vernier Calipers. The least count of Digital Vernier Calipers is 0.01 mm.

Screw gauge:

A screw gauge is an instrument that is used to measure small lengths with accuracy greater than a Vernier Caliper. It is also called a micrometer screw gauge.

 

Construction:

A simple screw gauge consists of a U-shaped metal frame with a metal stud at its one end. A hollow cylinder (or sleeve) has a millimeter scale over it along a line called the index line parallel to its axis. The hollow cylinder acts as a nut. It is fixed at the end of the U-shaped frame opposite the stud. A Thimble has a threaded spindle inside it. As the thimble completes one rotation, the spindle moves 1 mm along the index line. It is because the distance between consecutive threads on the spindle is 1 mm. This distance is called the pitch of the screw on the spindle.

 

Least count of screw gauge:

Least count = pitch of the screw gauge Least count ÷ no. of division on circular scale                  = 1mm ÷ 100 => 0.01 mm = 0.001 cm

Thus, the least count of the screw gauge is 0.01 mm or 0.001 cm.

 

Working of a screw gauge:

The first step is to find the zero error of the screw gauge.

 

 Zero error:

To find the zero error, close the gap between the spindle and the stud of the screw gauge by rotating the ratchet in the clockwise direction. If zero of the circular scale coincides with the index line, then the zero error will be zero.

 

Positive zero error:

Zero error will be positive if zero of the circular scale is behind the index line. In this case. Multiply the number of divisions of the circular scale that has not crossed the index line with the least count of screw gauge to find zero error.

 

Negative zero error:

Zero error will be negative if zero of the circular scale has crossed the index line. In this case, multiply the number of divisions of the circular scale that has crossed the index line with the least count of screw gauge to find the negative zero error.

 

Tidbits

Relative sizes of molecules and micro-organisms.

 

MINI EXERCISE

1. What is the least count of a screw gauge?

 Ans: The least count of the screw gauge is 0.01 mm or 0.001 cm.

 

2. What is the pitch of your laboratory screw gauge?

Ans: The pitch of our laboratory screw gauge is 1mm.

 

3. What is the range of your laboratory screw gauge?

(a) Vernier Calipers  (b) Screw Gauge

Ans: The range of our laboratory screw gauge is 100 mm.

 

4. Which one of the two instruments is more precise and why?

(a) Vernier Calipers (b) Screw Gauge

Ans: The least count of Vernier calipers is 0.01cm while the least count of screw gauge is 0.001 cm. The Vernier calipers measure the length with an accuracy of 0.01 cm. The screw gauge measures the length with an accuracy of 0.001 cm. therefore screw gauge is a more precise instrument.

 

USEFUL INFORMATION

The least count of the ruler is 1mm. It is 0.1mm for Vernier Calipers and 0.01mm for micrometer screw gauge. Thus, measurements taken by a micrometer screw gauge are the most precise than the other two. 

 

Beam balance:

Pots were used to measure grain in various parts of the world in ancient times. However, balances were also in use by the Greeks and Romans. Beam balances are still in use in many places. In a beam balance, the unknown mass is placed in one pan. It is balanced by putting known masses in the other pan. Today people use many types of mechanical and electronic balances.

Physical balance:

A physical balance is used in the laboratory to measure the mass of various objects by comparison.

 

Construction and working:

 It consists of a beam resting at the Centre on a fulcrum.

The beam carries scale pans over the hooks on either side. An unknown mass is placed on the left pan. Find some suitable standard masses that cause the pointer to remain at zero on raising the beam.

 

MINI EXERCISE

 

1. What is the function of balancing screws in a physical balance?

 Ans: We use the balancing screws to remove the zero error of the physical balance. Balancing screws in a physical balance are used to bring the pointer to zero position.

OR (Second answer)

There are two screws on the physical balance. One is on the left side and the other is on the right side of the physical balance. If the pointer is not in the middle of the scale, we move these screws forwards or backward to bring the pointer to the middle of the scale. This is done before we put any mass or weight in either of the pans.

In other words, we use the screws to remove the zero error of the physical balance.

 

2. On what pan do we place the object and why?

Ans: We Place the object into the left pane. In the case of physical balance, there the body is fixed and the weights have to be added in denominations. So only for convenience, we put the weights on the right pan after keeping the body on the left pan. I suppose a left-handed person weighs in a physical balance then no harm in placing the body in the right pan and putting the denominations of the weights on the left pan.

 

Lever balance:

A lever balance consists of a system of levers. When the lever is lifted placing the object in one pan and standard masses on the other pan, the pointer of the lever system moves. The pointer is brought to zero by varying standard masses.

 

Electronic balance:

Electronic balances come in various ranges; milligram ranges, gram ranges, and kilogram ranges. Before measuring the mass of a body, it is switched ON and its reading is set to zero. Next place the object to be weighed. The reading on the balance gives you the mass of the body placed over it.

The most Accurate Balance:

The mass of a one-rupee coin is done using different balances as given below:

(a) Beam Balance:

Let the balance measures the coin's mass = 3.29 A sensitive beam balance may be able to detect a change as small as 0.1 g or 100 mg.

(b) Physical Balance:

Let the balance measure the coin's mass = 3.24 g

The least count of the physical balance may be as small as 0.01 g of 10 mg. Therefore, its measurement would be more precise than a sensitive beam -balance.

(c) Electronic Balance:

Let the balance measure the coin's mass = 3.247 g Least count of an electronic balance is 0.001 g or 1mg. Therefore, its measurement would be more precise than a sensitive physical balance.

Conclusion:

Thus, electronic balance is the most sensitive balance in the above balances.

USEFUL INFORMATION

The precision of a balance in measuring the mass of an. the object is different for different balances. A sensitive balance cannot measure large masses. Similarly, a balance that measures large masses cannot be sensitive.

Some digital balances measure an even smaller difference of the order of 0.0001 g or 0.1 mg. Such balances are considered the most precise balance.

Stopwatch:

A stopwatch is used to measure the time interval of an event.

 

Mechanical stopwatch:

A mechanical stopwatch can measure a time interval up to a minimum of 0.1 seconds.

The least count of the mechanical stopwatch is 0.1 seconds.

 

Digital stopwatch:

Digital stopwatches commonly used in laboratories can measure a time interval as small as 1/100 second or 0.01 second.

The least count of the digital stopwatch is 0.01 seconds.

 

How to use a Stopwatch:

Use of a mechanical stopwatch:

A mechanical stopwatch has a knob that is used to wind the spring that powers the watch. It can also be used as a start-stop and reset button. The watch starts when the knob is pressed once. When pressed the second time, it stops the watch while the third press brings the needle back to zero position.                                                                                       

 

Use of a digital stopwatch:

          The digital stopwatch starts to indicate the time lapsed as the start/stop button is pressed. As soon as the start/stop button is pressed again. It stops and indicates the time interval recorded by it between the start and stop of an event. A reset button restores its initial zero settings.

 

LABORATORY SAFETY EQUIPMENT

A school laboratory must-have safety equipment such as:

• Waste-disposal basket
• Fire extinguisher. S
• Fire alarm.
• First Aid Box.
• Sand and water buckets.
• Fire blanket to put off the fire.
• Substances and equipment that need extra care must bear proper warning signs such as given below:

Measuring cylinder:

 A measuring cylinder is a graduated glass cylinder marked in milliliters. It is used to measure the volume of a liquid and also to find the volume of an irregular-shaped solid object. It has a scale along its length that indicates the volume in milliliter (mL).

Measuring cylinders have different capacities from 100 mL to 2500 ml.

 

How to use a measuring cylinder:

While using a measuring cylinder, it must be kept vertical on a plane surface. Take a measuring cylinder. Place it vertically on the table. Pour some water into it. Note that the surface of the water is curved. The meniscus of the most liquids curves downwards while the meniscus of mercury curves upwards.

 

The correct method to note the level of a liquid:

The correct method to note the level of a liquid in the cylinder is to keep the eye at the same level as the meniscus of the liquid. It is incorrect to note the liquid level keeping the eye above the level of the liquid.

When the eye is above the liquid level, the meniscus appears higher on the scale. Similarly, when the eye is below the liquid level, the meniscus appears lower than the actual height of the liquid.

Measuring the volume of an irregular shaped solid:

A measuring cylinder can be used to find the volume of a small irregular-shaped solid that sinks in water. Let us find the volume of a small stone. Take some water in. a graduated measuring cylinder. Note the volume V, of water in the cylinder. Tie the solid with a thread. Lower the solid into the cylinder till it is fully immersed in water. Note the volume V_i of water and the solid. The volume of the solid will be V_f — V_i

LABORATORY SAFETY RULES

The students should know what to do in case of an accident. The charts or posters are to be displayed in the laboratory to handle situations arising from any mishap or accident. For your safety and the safety of others in the laboratory, follow the safety rules given below:

1. Do not carry out any experiment without the permission of your teacher.
2. Do not eat, drink, play or run in the laboratory.
3. Read the instructions carefully to familiarize yourself with the possible hazards before handling equipment and materials.
4. Handle equipment and materials with care.
5. Do not hesitate to consult your teacher in case of any doubt.
6. Do not temper the electrical appliances and other fittings in the laboratory.
7. Report any accident or injuries immediately to your teacher.

Significant figures:

          All the accurately known digits and the first doubtful digit in an expression are called significant figures. It reflects the precision of a measured value of a physical quantity.

 The accuracy in measuring a physical quantity depends upon various factors:

1. The quantity of the measuring instrument
2. The skill of the observer
3. The number of observations made

 

 For example, a student measures the length of a book as 18cm using a measuring tape. The numbers of significant figures in his/her measured value are two. The left digit 1 is the accurately known digit. While the digit 8 is the doubtful digit for which the student may not be sure.

 

Rules for determining significant figures:
The following rules help identify significant figures:

1. Non-zero digits are always significant.
2. Zeros between two significant figures are also significant.
3. Final or ending zeros on the right in the decimal fraction are significant.
4. Zeros are written on the left side of the decimal point to space the decimal point is not significant.
5. In whole numbers that end in one or more zeros without a decimal point. These zeros may or may not be significant. In such cases, it is not clear which zeros serve to locate the position value and which are parts of the measurement. In such a case, express the quantity using scientific notation to find the significant zero.

 

RULES TO FIND THE SIGNIFICANT DIGITS INA MEASUREMENT

• Digits other than zero are always significant.

 27 has 2 significant digits.

275 has 3 significant digits.

 

• Zeros between significant digits are also significant.

2705 has 4 significant digits.

 

• Final zero or zeros after the decimal are significant

 275.00 has 5 significant digits.

 

• Zeros used for spacing the decimal point are not significant here zeros are placeholders only.

 0.03 has 1 significant digit.    

0.027 has 2 significant digits.

ROUNDING THE NUMBERS

 

1. If the last digit is less than 5 then it is simply dropped. This decreases the number of significant digits in the figure.

For example,

1.943 is rounded to 1.94 (3 significant figures)

 

2. If the last digit is greater than 5, then the digit on its left is increased by one. This also decreases the number of significant digits in the figure.

For example,

1.47 is rounded to two significant digits 1.5

 

3. If the last digit is 5, then it is rounded to get nearest even number.

For example,

 1.35 is rounded to 1.4 and 1.45 is also rounded to 1.4