1. Here are results statistics for the most recent examination series. Due to the Covid-19 pandemic, no examinations were held in June 2020. To enable as many candidates as possible to progress to the next stage of their lives, we asked teachers to predict grades.
2. Results in Chemistry. View aims and scope Submit your article Guide for authors. View editorial board. View aims and scope. Explore journal content Latest issue Articles in press Article collections All issues. Sign in to set up alerts. In progress (January 2021) Volume 2.

Results in Chemistry is an open access journal offering authors the opportunity to publish in all fundamental and interdisciplinary areas of chemistry and related fields. Papers of experimental, theoretical and computational nature are all welcome.

Overview: In reporting numerical results, it is important to include the correct number of significant digits. While determining the correct number of digits to include is a straightforward process, beginning students often overlook this important detail. Here we outline the rules involved in determining the appropriate number of digits to include when reporting results of calculations and experimental measurements.

Skills:

• Reporting scientific results with the appropriate number of significant digits.

New terms:

• Significant Figures
• Precision
• Accuracy

Defining the Terms Used to Discuss Significant Figures

Significant Figures: The number of digits used to express a measured or calculated quantity.
By using significant figures, we can show how precise a number is. If we express a number beyond the place to which we have actually measured (and are therefore certain of), we compromise the integrity of what this number is representing. It is important after learning and understanding significant figures to use them properly throughout your scientific career.

Precision:A measure of how closely individual measurements agree with one another.
Accuracy: Refers to how closely individual measurements agree with the correct or true value.

Digits that are Significant

1. Non-zero digits are always significant.
2. Any zeros between two non-zero digits are significant.
3. A final zero or trailing zeros in the decimal portion ONLY are significant.

Examples:

How many significant figures are in:1. 12.548, 2. 0.00335, 3. 504.70, 4. 4000

1. There are 5. All numbers are significant.
2. There are 3. The zeros are simply placeholders and locate the decimal. They are not trailing zeros. They are not significant.
3. There are 5. The two zeros are not simply placeholders. One is between two significant digits and the other is a final, trailing zero in the decimal portion. Hence, they are both significant.
4. This is a bit confusing. It is somewhere between 1 and 4. In order to clarify, we need to convert this to scientific notation. If it were 4 x 10³, there is one significant figure. If it were 4.000 x 10³, then there are 4 significant figures.

Rules for Using Significant Figures

• For addition and subtraction, the answer should have the same number of decimal places as the term with the fewest decimal places.
• For multiplication and division, the answer should have the same number of significant figures as the term with the fewest number of significant figures.
• In multi-step calculations, you may round at each step or only at the end.
• Exact numbers, such as integers, are treated as if they have an infinite number of significant figures.
• In calculations, round up if the first digit to be discarded is greater than 5 and round down if it is below 5. If the first discarded digit is 5, then round up if a nonzero digit follows it, round down if it is followed by a zero.

More Examples:

Addition and Subtraction.12.793 + 4.58 + 3.25794 = 20.63094

• With significant figures it is 20.63 since 4.58 has 2 decimal places, which is the least number of decimal places.

Multiplication and Division.56.937/0.46 = 130.29782609

• With significant figures, the final value should be reported as 1.3 x 10² since 0.46 has only 2 significant figures. Notice that 130 would be ambiguous, so scientific notation is necessary in this situation.

Tidiness at the end of a calculation.

So you have carried out a calculation that requires a series of seven or eight mathematical operations and at the end, after punching everything into your calculator, you see the result '14.87569810512...'. The question you should ask yourself is how many digits to include when reporting your final answer.

It is at this point that you must refer back to the quality of the data you were given (i.e., how many significant digits are included with the given data). We illustrate this here with one final example.

Three scientists determine the mass of the samesample of FeCl

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₃. Scientist A works in a field laboratory and carries a portable balance for determining the sample mass, the balance can determine masses to the nearest +/- 0.1 g. Scientist B has a better, but still somewhat crude balance, which reports the mass to the nearest +/- 0.01 g. Scientist C has a balance, like the analytical balances you will find in chemistry laboratories at WU, that can determine sample masses to the nearest +/- 0.0001 g. If each scientist wants to indicate the total number of moles of FeCl₃ in the sample, how will each do this in a way that reflects the precision of the instrumentation they are using? The three scientists all use the atomic masses suggested by IUPAC (International Union of Pure and Applied Chemistry), which are included in the table below.

Scientist B
given data	sample mass: 19.0 g Fe atomic mass: 55.847 g/mol Cl atomic mass: 35.4527 g/mol	sample mass: 18.99 g Fe atomic mass: 55.847 g/mol Cl atomic mass: 35.4527 g/mol	sample mass: 18.9925 g Fe atomic mass: 55.847 g/mol Cl atomic mass: 35.4527 g/mol
0.117 mol FeCl3	0.1171 mol FeCl3	0.11709 mol FeCl3
Why?	The balance used for the mass determination limits the result to 3 significant digits.	The quality of the instrumentation is better, than that used by Scientist A, but the result is still limited to only 4 significant digits.	Why not 6 significant digits in the reported result? This time the answer is limited by the uncertainty in the atomic mass of Fe, which is known to 5 significant digits!

This brings up an interesting question. Why is the atomic mass of chlorine known to 6 significant figures, while that of iron is only known to 5 significant figures? Click here for an explanation.

More Examples

• Examples of rounding to the correct number of significant figures with a 5 as the first non-significant figure
  
  • Round 4.7475 to 4 significant figures: 4.7475 becomes 4.748 because the first non-significant digit is 5, and we round the last significant figure up to 6 to make it even.
  
  
  • Round 4.7465 to 4 significant figures: 4.7465 is 4.746 because the first non-significant digit is 5 and since the last significant digit is even, we leave it alone.
    
• An example of a calculation where you can 'lose' significant figures doing an operation.
  The mass of ¹⁹F is 18.99840 u. How much mass is converted to energy when a ¹⁹F atom is assembled from its constituent protons, neutrons, and electrons?
  ¹⁹F 9 p⁺ + 9 e^- + 10 n⁰
  

Return to the Chemistry Subject Index

Today we are continuing our popular blog series “How to Study …” focusing on “How to Study Chemistry”. In today’s post we will help you to discover tips and techniques to help you improve your Chemistry results. Don’t forget to have a look at our previous issues on how to study Mathematics, History, and Biology.

Chemistry is a subject that is often studied alongside Physics. However, it is important to remember that the two subjects are very different. With this in mind, we have distinguished and identified the best methods and study techniques for each.

How to Study Chemistry

#1: Read The Material Before Going To Class

The method known as ‘Flipped Classroom’ or ‘Class Reversed’ is a growing trend in all subjects, including science. However, its effect in learning Chemistry can be seen twofold. The technique encourages students to study the lesson before going to class. This concept familiarises the student with the subject content making the class much easier to follow. Students can then consolidate that knowledge and use class time to raise important questions.

#2: Understanding Rather Than Memorising

William James said: “The essence of genius is to know what to overlook.” We cannot agree more! You have to be selective with what you memorise. When we study, efforts should focus on understanding concepts rather than memorising every last detail. Once we have gathered the important facts, we can implement this selective memory method. But remember, under no circumstances should memorisation replace understanding.

#3: Use Flashcards

The course is full of Chemical symbols, Chemical formulas and very scientific language. Interpreting all of these concepts correctly is key to your success in Chemistry. Although this may seem like an obvious point, large numbers of students fail Chemistry each year because they underestimate the importance of understanding this complex subject.

With this in mind, study sheets or flashcards are ideal for organising and storing chemical symbols and formulas on. Once you have created a good set of flashcards containing the periodic table of the elements and formulas, memorisation will become much easier.

#4: Take Notes

It is not enough to simply pay attention in class. In Chemistry, it is necessary to write down everything and understand what you taking notes on. Formulas and equations are far easier to understand once written down and presented in the right way. When notes are compiled and stored in an organised fashion, it is easier to determine what you do and don’t understand. If you want a simple way to create some great notes wherever you are, try our Online Notes tool.

#5: Practice Daily

Continuing with the previous point, one of the key areas in the study of Chemistry is practice. Solving equations and practical problems should be a feature part of your study routine. Test your knowledge with sample Chemistry tests on a regular basis. This will prepare you for your exam and assesses your level of understanding of Chemistry to date. Moreover, as we mentioned in the subject of Biology, it is important to go to the lab as often as possible. There is no substitute for hands on experience. It strengthens our knowledge of Chemistry in a practical environment.

Discover How To Study Chemistry

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Finally, we would like to emphasise that, although we have separated these study methods into 5 sections, these are not stand alone ways to succeed. Rather, when used together, they will increase effectiveness of your study time. In addition, Chemistry includes many fields of study, each with its own particulars, so it is necessary that you evaluate your own strengths and weaknesses and choose the study method that best suits you.

Some of these fields have a heavy load of Maths or Physics, so mastering these subjects is also crucial. With this in mind, don’t forget that with ExamTime, you can enter mathematical and chemical symbols using the LaTeX language resources. This will facilitate the introduction of formulas, equations and other mathematical concepts.

Do you have any other tips on how to study Chemistry? If so, share them with us in the comments section below!

Results In Chemistry

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