Measurement Uncertainty-Significant Figures,Accuracy, Precision Solved Examples

In Chemistry, students often deal with experimental data and theoretical calculations. Most of the data is present in an extremely large number of quantum. This uncertainty in measurement is the range of possible values within which the true/real value of the measurement exists.

There are practical ways to handle these figures with convenience and present the given data as realistically as possible.

Scientific Notation

As discussed above, atoms and molecules have very low masses and are present in exceedingly large numbers. We are here dealing with numbers as large as 602,200,000,000,000,000,000,000 for the molecules of just 2 g of H2 hydrogen gas and as small as 0.00000000000000000000000166 g which is the mass of a hydrogen atom. On a similar scale exist the values of constants such as the speed of light, Planck’s constant, electric charge of particles, etc.

Thus, when handling numbers involving such scales of zeroes, it becomes extremely difficult for simple calculations of addition, subtraction, multiplication, and division. To solve these issues, scientists have developed a scientific notation for such numbers.

Scientific Notation here is the exponential notation in which one can represent a given number in the form of N × 10n, where N is a digit term that ranges between 1.000… and 9.999…, and n is an exponent of positive or negative values. Accordingly, one can write 2702.0109 as 2.7020109 × 103 in scientific notation. It can be observed that once shifted the decimal point three places to the left and thus added the exponent (3) of 10 to the scientific notation. Similarly, write 0.00001008565 as 1.008565 ×  10-5. Here, the decimal point is moved to the right by five places as the (-5) exponent of 10 is in the scientific notation.

Multiplication and Division

Both Multiplication and Division follow the same rules that exist for exponential numbers. Let’s take a look at some examples to understand how multiplication and division is done,

Example 1: (4.2342 × 1019) × (7.32 × 105)

Solution:

(4.2342 × 1019) × (7.32 × 105)

= (4.2342 × 7.32) × 10(19+5)

= 30.994344 × 1024

= 3.099 × 1025

Example 2: (6.23 × 106) ÷ (8.33 × 10-2)

Solution:

(6.23 × 106) ÷ (8.33 × 10-2)

= (6.23 ÷ 8.33) × 106-(-2)

= (0.74789) × 108

= 7.4789 × 107

Addition and Subtraction

For Addition and Subtraction, first, ensure if the numbers are present in the same exponent. After that, the digit terms (coefficients) can be added or subtracted as required.

Example 1: (5.12 × 103) + (6.84 × 105)

Solution:

(5.12 × 103) + (6.84 × 105)

= (5.12 × 103) + (684 × 103)

= (5.12 + 684) × 103

= 689.12 × 103

= 6.8912 × 105

Example 2: (2.57 × 105) – (9.46 × 103)

Solution:

(2.57 × 105) – (9.46 × 103)

= (2.57 × 105) – (0.0946 × 105)

= (2.57 + 0.0946) × 105

= 2.4757 × 105

Significant Figures

All experimental measurements have some uncertainty present due to the drawbacks of the measuring instrument and lack of accuracy in observation. For example, when observed the mass of an object to be 15 grams on a platform balance. However, the same object may weigh 15.239 grams on an analytical scale. Thus one can always not correctly tell the exact measurement. This uncertainty in the given experimental or calculated values is shown by the number of significant figures.

Significant Figures are the digits that are known with certainty plus one which is estimated or uncertain. The uncertainty is thus shown by writing certain digits and the last uncertain digit. For example, if the temperature of the room is 35.2 °C, consider 35 as certain and 2 as uncertain. The uncertainty in this last digit is +1. If it is not stated, consider +1 in the last digit directly.  

Rules for deciding the number of significant figures in a given measurement.

  1. All Non-zero digits are to be considered significant. For example, 123 has three significant figures, while 0.123 also has three significant figures.
  2. Zeroes preceding the first non-zero aren’t significant. These zeroes indicate the position of the given decimal point. Thus, 0.02 has one significant figure and 0.000027 also has just two significant figures.
  3. Zeroes between any two non-zero digits are significant. Thus 9.003 has four significant figures.
  4. Zeroes at the end or on the right of a number (if they are on the right of the decimal point) are significant. For example, 0.500 ml has three significant figures. However, terminal zeroes are not significant if there isn’t a decimal point. For example, 9000 has only one significant figure, but 9000. has four significant figures, and 9000.0 has five significant figures. These numbers are better off represented in scientific notation. We would rather express 9000 as 9 × 103 for one significant figure or 9.00 × 103 for three significant figures.
  5. Exact numbers can be represented in infinite significant figures. Like 50 can be written as 50.0000000 or 734 can be written as 743.000000000 and so on. In scientific notation, all digits are significant. For example, 3.545 × 10-2 has four significant figures while 9.43 × 106 has three significant figures.

Accuracy and Precision

Precision stands for the closeness of different measurements for the same quantity. Accuracy is the consensus of a particular value to the true value of the measurement.

For example, suppose three students Alex, Bob, and Carol are measuring the length of the physics textbook. The true length that is known of the book is 29.5 cm. Alex measures and reports two values 28.0 cm and 28.2 cm. Both these values are precise as they are close to each other but not accurate. Bob measures and reports two values 28.5 cm and 30.5 cm. The average of these values is the true value but this observation though accurate is not precise. Carol repeats this experiment and measures 29.4 cm and 29.6 cm. Both these values are precise and accurate as they are close to each other and the average is the true value.

 True Value = 29.5 cm
 1st Observation2nd Observation Average of bothPreciseAccurate
Alex28.0 cm28.2 cm28.1 cmYesNo
Bob28.5 cm30.5 cm29.5 cmNoYes
Carol29.4 cm29.6 cm29.5 cmYesYes

Sample Problems

Question 1: What is Dimensional Analysis? Give an example.

Answer:

When dealing with calculations, we often need to convert units from one system to another. The method to do so is called factor label method or unit factor method or dimensional analysis

For example, to find the length of a pen of 5 inches in cm.

By convention, 1 inch = 2.54 cm.

From this equivalence, write 1 inch / 2.54 cm = 1 = 2.54 cm / 1 inch. This means that both these are unit factors and are here considered equal to 1. Thus, now multiply 5 inches to this to calculate the measurement in cm. 

Therefore, 5 × (2.54 cm / 1 inch) = 12.7 cm.

Thus, the length of the pen in cm is 12.7 cm.

Question 2: What is Scientific notation? Write 7654630000210000 in scientific notation.

Answer:

Scientific Notation is the exponential notation in which we can represent a given number in the form of N x 10^n, where N is a digit term that ranges between 1.000… and 9.999…, and n is an exponent of positive or negative values. 

For example, we can write 7630210000 as 7.653021 × 109 in scientific notation. 

Question 3: What is the difference between Precision and Accuracy?

Answer:

Precision stands for the closeness of different measurements for the same quantity. Accuracy is the consensus of a particular value to the true value of the measurement. Thus, precision means how close the measurements are and accuracy stands for how correct the values are. 

Question 4: The exact weight of an object is 2.50 kg. A student named David measured 2.46 kg, 2.49 kg, and 2.52 kg respectively. Comment.

Answer:

David’s measurements are 2.46 kg, 2.49 kg and 2.52 kg. The average of these values is 2.49 kg. Considering the true value being 2.50 kg, we can comment that the measurements are accurate, but not precise as 2.46 kg and 2.52 kg are not close values. 

Question 5: Multiply 4.3545 × 1.9. Calculate the answer in terms of significant figures.

Answer:

4.3545 × 1.9 = 8.27355.

However, when considered in terms of significant figures, in these operations, the result must be reported with no more significant figures as in the measurement with the few significant figures.

Thus, one can have maximum only two significant figures as 1.9 has only two significant figures. 

Therefore, 4.3545 × 1.9 = 8.2, where 8.2 has only 2 significant figures. 

Question 6: Calculate the number of seconds in 3 days. 

Answer:

By convention, 1 day = 24 hours.

From this equivalence, write 1 day / 24 hours = 1 = 24 hours / 1 day. This means that both these are unit factors and are here considered equal to 1. 

Similarly, find the equivalence from hours to seconds. 

Therefore, 

3 days = (3 days × (24 hours / 1 day) × (60 min / 1 hour) × (60 s / 1 min)) seconds 

3 days = (3 × 24 × 60 × 60) seconds

3 days = 259200 seconds

3 days = 2.592 × 105 seconds.

Thus, 3 days have 2.592 × 105 seconds.

Question 7: Are zeroes considered significant numbers?

Answer:

Zeroes preceding the first non-zero aren’t significant. These zeroes indicate the position of the given decimal point. Thus, 0.02 has one significant figure and 0.000027 also has just two significant figures. Zeroes between any two non-zero digits are significant. Thus 9.003 has four significant figures. Zeroes at the end or on the right of a number (if they are on the right of the decimal point) are significant.

Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.

CBSE Class 11 Chemistry Syllabus

CBSE Class 11 Chemistry Syllabus is a vast which needs a clear understanding of the concepts and topics. Knowing CBSE Class 11 Chemistry syllabus helps students to understand the course structure of Chemistry.

Unit-wise CBSE Class 11 Syllabus for Chemistry

Below is a list of detailed information on each unit for Class 11 Students.

UNIT I – Some Basic Concepts of Chemistry

General Introduction: Importance and scope of Chemistry.

Nature of matter, laws of chemical combination, Dalton’s atomic theory: concept of elements,
atoms and molecules.

Atomic and molecular masses, mole concept and molar mass, percentage composition, empirical and molecular formula, chemical reactions, stoichiometry and calculations based on stoichiometry.

UNIT II – Structure of Atom

Discovery of Electron, Proton and Neutron, atomic number, isotopes and isobars. Thomson’s model and its limitations. Rutherford’s model and its limitations, Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, de Broglie’s relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p and d orbitals, rules for filling electrons in orbitals – Aufbau principle, Pauli’s exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half-filled and completely filled orbitals.

UNIT III – Classification of Elements and Periodicity in Properties

Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements -atomic radii, ionic radii, inert gas radii, Ionization enthalpy, electron gain enthalpy, electronegativity, valency. Nomenclature of elements with atomic number greater than 100.

UNIT IV – Chemical Bonding and Molecular Structure

Valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, concept of hybridization, involving s, p and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules(qualitative idea only), Hydrogen bond.

UNIT V – Chemical Thermodynamics

Concepts of System and types of systems, surroundings, work, heat, energy, extensive and intensive properties, state functions. First law of thermodynamics – internal energy and enthalpy, measurement of U and H, Hess’s law of constant heat summation, enthalpy of bond dissociation, combustion, formation, atomization, sublimation, phase transition, ionization, solution and dilution. Second law of Thermodynamics (brief introduction)
Introduction of entropy as a state function, Gibb’s energy change for spontaneous and nonspontaneous processes.
Third law of thermodynamics (brief introduction).

UNIT VI – Equilibrium

Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium – Le Chatelier’s principle, ionic equilibrium- ionization of acids and bases, strong and weak electrolytes, degree of ionization,
ionization of poly basic acids, acid strength, concept of pH, hydrolysis of salts (elementary idea), buffer solution, Henderson Equation, solubility product, common ion effect (with illustrative examples).

UNIT VII – Redox Reactions

Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, in terms of loss and gain of electrons and change in oxidation number, applications of redox reactions.

UNIT VIII – Organic Chemistry: Some basic Principles and Techniques

General introduction, classification and IUPAC nomenclature of organic compounds. Electronic displacements in a covalent bond: inductive effect, electromeric effect, resonance and hyper conjugation. Homolytic and heterolytic fission of a covalent bond: free radicals, carbocations, carbanions, electrophiles and nucleophiles, types of organic reactions.

UNIT IX – Hydrocarbons

Classification of Hydrocarbons
Aliphatic Hydrocarbons:
Alkanes – Nomenclature, isomerism, conformation (ethane only), physical properties, chemical reactions.
Alkenes – Nomenclature, structure of double bond (ethene), geometrical isomerism, physical properties, methods of preparation, chemical reactions: addition of hydrogen, halogen, water, hydrogen halides (Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition.
Alkynes – Nomenclature, structure of triple bond (ethyne), physical properties, methods of preparation, chemical reactions: acidic character of alkynes, addition reaction of – hydrogen, halogens, hydrogen halides and water.

Aromatic Hydrocarbons:

Introduction, IUPAC nomenclature, benzene: resonance, aromaticity, chemical properties: mechanism of electrophilic substitution. Nitration, sulphonation, halogenation, Friedel Craft’s alkylation and acylation, directive influence of functional group in monosubstituted benzene. Carcinogenicity and toxicity.

To know the CBSE Syllabus for all the classes from 1 to 12, visit the Syllabus page of CBSE. Meanwhile, to get the Practical Syllabus of Class 11 Chemistry, read on to find out more about the syllabus and related information in this page.

CBSE Class 11 Chemistry Practical Syllabus with Marking Scheme

In Chemistry subject, practical also plays a vital role in improving their academic scores in the subject. The overall weightage of Chemistry practical mentioned in the CBSE Class 11 Chemistry syllabus is 30 marks. So, students must try their best to score well in practicals along with theory. It will help in increasing their overall academic score.

CBSE Class 11 Chemistry Practical Syllabus

The experiments will be conducted under the supervision of subject teacher. CBSE Chemistry Practicals is for 30 marks. This contribute to the overall practical marks for the subject.

The table below consists of evaluation scheme of practical exams.

Evaluation SchemeMarks
Volumetric Analysis08
Salt Analysis08
Content Based Experiment06
Project Work04
Class record and viva04
Total30

CBSE Syllabus for Class 11 Chemistry Practical

Micro-chemical methods are available for several of the practical experiments. Wherever possible such techniques should be used.

A. Basic Laboratory Techniques
1. Cutting glass tube and glass rod
2. Bending a glass tube
3. Drawing out a glass jet
4. Boring a cork

B. Characterization and Purification of Chemical Substances
1. Determination of melting point of an organic compound.
2. Determination of boiling point of an organic compound.
3. Crystallization of impure sample of any one of the following: Alum, Copper Sulphate, Benzoic Acid.

C. Experiments based on pH

1. Any one of the following experiments:

  • Determination of pH of some solutions obtained from fruit juices, solution of known and varied concentrations of acids, bases and salts using pH paper or universal indicator.
  • Comparing the pH of solutions of strong and weak acids of same concentration.
  • Study the pH change in the titration of a strong base using universal indicator.

2. Study the pH change by common-ion in case of weak acids and weak bases.

D. Chemical Equilibrium
One of the following experiments:

1. Study the shift in equilibrium between ferric ions and thiocyanate ions by increasing/decreasing the concentration of either of the ions.
2. Study the shift in equilibrium between [Co(H2O)6] 2+ and chloride ions by changing the concentration of either of the ions.

E. Quantitative Estimation
i. Using a mechanical balance/electronic balance.
ii. Preparation of standard solution of Oxalic acid.
iii. Determination of strength of a given solution of Sodium hydroxide by titrating it against standard solution of Oxalic acid.
iv. Preparation of standard solution of Sodium carbonate.
v. Determination of strength of a given solution of hydrochloric acid by titrating it against standard Sodium Carbonatesolution.

F. Qualitative Analysis
1) Determination of one anion and one cation in a given salt
Cations‐ Pb2+, Cu2+, As3+, Al3+, Fe3+, Mn2+, Ni2+, Zn2+, Co2+, Ca2+, Sr2+, Ba2+, Mg2+, NH4 +
Anions – (CO3)2‐ , S2‐, NO2 , SO32‐, SO2‐ , NO , Cl , Br, I‐, PO43‐ , C2O2‐ ,CH3COO
(Note: Insoluble salts excluded)

2) Detection of ‐ Nitrogen, Sulphur, Chlorine in organic compounds.

G) PROJECTS
Scientific investigations involving laboratory testing and collecting information from other sources.

A few suggested projects are as follows:

  • Checking the bacterial contamination in drinking water by testing sulphide ion
  • Study of the methods of purification of water.
  • Testing the hardness, presence of Iron, Fluoride, Chloride, etc., depending upon the regional
    variation in drinking water and study of causes of presence of these ions above permissible
    limit (if any).
  • Investigation of the foaming capacity of different washing soaps and the effect of addition of
    Sodium carbonate on it.
  • Study the acidity of different samples of tea leaves.
  • Determination of the rate of evaporation of different liquids Study the effect of acids and
    bases on the tensile strength of fibres.
  • Study of acidity of fruit and vegetable juices.

Note: Any other investigatory project, which involves about 10 periods of work, can be chosen with the approval of the teacher.

Practical Examination for Visually Impaired Students of Class 11

Below is a list of practicals for the visually impaired students.

A. List of apparatus for identification for assessment in practicals (All experiments)
Beaker, tripod stand, wire gauze, glass rod, funnel, filter paper, Bunsen burner, test tube, test tube stand,
dropper, test tube holder, ignition tube, china dish, tongs, standard flask, pipette, burette, conical flask, clamp
stand, dropper, wash bottle
• Odour detection in qualitative analysis
• Procedure/Setup of the apparatus

B. List of Experiments A. Characterization and Purification of Chemical Substances
1. Crystallization of an impure sample of any one of the following: copper sulphate, benzoic acid
B. Experiments based on pH
1. Determination of pH of some solutions obtained from fruit juices, solutions of known and varied
concentrations of acids, bases and salts using pH paper
2. Comparing the pH of solutions of strong and weak acids of same concentration.

C. Chemical Equilibrium
1. Study the shift in equilibrium between ferric ions and thiocyanate ions by increasing/decreasing
the concentration of eitherions.
2. Study the shift in equilibrium between [Co(H2O)6]2+ and chloride ions by changing the
concentration of either of the ions.

D. Quantitative estimation
1. Preparation of standard solution of oxalic acid.
2. Determination of molarity of a given solution of sodium hydroxide by titrating it against standard
solution of oxalic acid.

E. Qualitative Analysis
1. Determination of one anion and one cation in a given salt
2. Cations – NH+4
Anions – (CO3)2-, S2-, (SO3)2-, Cl-, CH3COO-
(Note: insoluble salts excluded)
3. Detection of Nitrogen in the given organic compound.
4. Detection of Halogen in the given organic compound.

Note: The above practicals may be carried out in an experiential manner rather than recording observations.

We hope students must have found this information on CBSE Syllabus useful for their studying Chemistry. Learn Maths & Science in interactive and fun loving ways with ANAND CLASSES (A School Of Competitions) App/Tablet.

Frequently Asked Questions on CBSE Class 11 Chemistry Syllabus

Q1

How many units are in the CBSE Class 11 Chemistry Syllabus?

There are 9 units in the CBSE Class 11 Chemistry Syllabus. Students can access various study materials for the chapters mentioned in this article for free at ANAND CLASSES (A School Of Competitions).

Q2

What is the total marks for practicals examination as per the CBSE Class 11 Chemistry Syllabus?

The total marks for the practicals as per the CBSE Class 11 Chemistry Syllabus is 30. It includes volumetric analysis, content-based experiment, salt analysis, class record, project work and viva.

Q3

Which chapter carries more weightage as per the CBSE Syllabus for Class 11 Chemistry?

The organic chemistry chapter carries more weightage as per the CBSE Syllabus for Class 11 Chemistry.