Significant figures can be one of the most annoying and confusing aspects to VCE Chemistry. It doesn't have to be. Read the two sections below (take special note of section two), and you'll be cruising.

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**THE RULES FOR REPORTING ANSWERS TO THE CORRECT NUMBER OF SIGNIFICANT FIGURES**

When you are doing any sort of scientific calculations you need to be aware of significant figures, decimal places, and how accurately you can report your results.

Significant figures include every figure in the number except zeros that are used to place the decimal point.

Example. The following all have three significant figures:

a. 0.465

b. 0.0465

c. 15.0 (this zero is not placing the decimal point but makes the number more accurate than 15 so is significant)

When performing operations with numbers with different significant figures, one must be aware of the accuracy with which the answer can be reported. The following is a summary of the rules to use:

Addition and Subtraction

The answer should be given to the lowest number of decimal places of the original numbers

Eg: 53.06 – 52.1 = 1.0 (shown to 1 decimal place as 52.1 has 1 decimal place)

Multiplication and Division

The answer should be given to the lowest number of significant figures of the original numbers

Eg: 43 × 0.01 = 0.4 (shown to 1 significant figure as 0.01 has 1 significant figure)

The next two are not technically in the scope of the VCE course. But, if you want to make sure that you're always right, especially when dealing with pH calculations, read on.

Logarithms

The answer should be given to the same number of decimal places as there are significant figures in the number that you are applying the logarithm to.

log_{10} 11.2 = 1.049 (shown to 3 decimal places as 11.2 has 3 significant figures)

Exponentials

The answer should be given to the same number of significant figures as decimal places in the exponent.

10^{0.42} = 2.6 (shown to 2 significant figures as 0.42 has 2 decimal places)

Note that multiplication and division take priority over addition and subtraction so would be reported to the correct number of significant figures.

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**SIGNIFICANT FIGURES IN THE CONTEXT OF VCE**

The way VCE works is that they only check that you have the correct number of significant figures for one question in the paper. The catch is, they don't tell you which one! So, you have to be careful with every question.

Say you have a volumetric analysis question involving multiple calculations. Ie: You get a question with parts a. to e.

Within each part of the question, always keep using the numbers on your calculator memory. Do NOT round at any stage within a part of question on your calculator. However, when writing down steps, it's good to show numbers to the correct number of significant figures so that when you reach the end of that part and have to state your answer, you can easily determine how many sig figs it's going to be.

If you have to use your answer from part a. in part b., for example, you then use the rounded answer that you wrote down, not the one on your calculator. You then proceed as above.

If you get into these habits early, you'll be fine in SACs and the exam!