Significant figures and the rules around them are a significant piece of knowledge that you will need if you are going into a scientific field. Significant figures deal with reporting a calculation as precise and accurate. According to the rules, a number determined through a calculation cannot be more precise or accurate than the numbers used to determine that calculation. To the standard person, this might sound confusing and unnecessary, but failure to follow significant figure procedures in medical and engineering fields can result in assumptions and catastrophic failures.
Significant figures can also be a considerable annoyance to deal with as you have to track everything throughout the calculation. As annoying as they are though, you cannot disregard it and must follow the rules strictly to ensure precision and accuracy within any calculation you do. Here are the basic rules of significant figures and the reasons why we need to learn them
Your calculation cannot be more precise than the digits given
When performing a calculation, the number of digits your answer should have should not be greater than the number with the lowest number of digits used in the calculation. An example of this would be to look at 20 – 8. Most of us will recognize that this is equal to 12, however looking at the significant digit rule, we can see that twenty has two significant figures, and eight has one.
Therefore, in our answer we are only allowed to use one significant digit. How could we write 12 down then? We must switch over to scientific notation to represent this. Because we can only use one digit, the answer would look like 1 x 102. You might notice that we left out the two from the 12, that is because 1.2 would have two significant figures and therefore is proper form. If we wrote the same equation as 20 – 8.0, both numbers now have two significant figures and the answer could be written as 12. Taking this one step further, if the equation was 20.0 – 8.00, both numbers now have three significant figures, therefore the answer would be written as 12.0. It is essential that you follow the significant figure rule when adding and subtracting.
The same rule applies for multiplication and division. When applying the significant figure rule, perform calculations as normal all the way till the end and then round the number to the number of significant figures required. When there are several steps required, do not round any of those numbers to the necessary number of significant figures till the very end. Now that you have an understanding of how significant figures work, let’s move on to easier ways to work with them.
Significant figure calculators
Are you tired of having to be constantly concerned about the number of significant figures your final answer should be? It can be difficult to solve a math problem when calculating equations with many numbers. Keeping track of significant figures can be daunting in situations like this. Luckily, there are calculators that help keep track of significant figures. This eliminates much of the hassle and allows you to stay focused on your thoughts and processes instead of worrying about how many decimal places your answer should be towards. Simply enter in the equation you would like calculated, and then enter the number of significant digits it should be, and then watch as the calculator gives you the exact answer that you want. Save yourself the time by using a simple calculator like this online.
The importance of significant figures
As stated before, it is important within the science fields that you are not more precise or accurate than the least accurate or precise number. In science, it is generally agreed upon that the last number digit in any figure is filled with uncertainty. If someone wrote 5, a person would ask, is it exactly 5 though? Is it maybe 5.2? Or maybe 4.8? There is a degree of uncertainty surrounding it, therefore we cannot be more precise as this can lead to plenty of errors. In engineering, especially when dealing with infrastructure; tensions, weights, and loads are measured and calculated.
By making these calculations more precise than we are able to, we run into an issue where we start to assume and therefore can end up making a critical error that can cause a collapse in the structure itself. Significant figures are important and must be followed.
Despite the frustrations of dealing with significant figures, they do exist for a reason. They help in the science fields to keep numbers accurate within their given range. Calculating with significant figures is something that can also be annoying, but thankfully you can use calculators to aid you in the process and help you along. What occupation are you getting into that requires significant figures?