The principles of mathematics are all about applying logic, executing calculation processes and using core concepts. When you talk about significant figures, there is a specific logic applied when you are calculating them in a number. To know about the correct count of figures, you should know about the rules and regulations applied. There are few basic principles through which you can determine the number of significant digits. If you are not clear about them, it would be hard to come up with the correct answers. Students who are studying mathematics should be absolutely clear about these principles. In this way, they would be able to provide the correct solutions in assignments and research submissions. Along with that, using the sig fig calculator is the best to round off a number to the desired number of significant digits.
Looking at the rules of significant figures
Every concept of mathematics is supported by a series. Let us glance at the rules applied in this relation.
All the non-zero numbers are significant
This is one of the important and easy to remember rules of significant figures. In accordance with this rule, all the numbers that are not zero will be counted as significant. Let us consider an example to gain a detailed understanding.
Consider that you have to determine the significant digits in the number “25668”. To start with, have a look at each digit of the number. The five digits in this number are “2”, “5”, “6”, “6” and “8”. If you have a look at all these five numbers, they are all non-zero. Considering this rule, it can be said that there are five significant digits in this number.
When you have these numbers in which all the digits are non-zero, it is not that hard to come up with the correct answer. As all the digits are above zero, each of them falls under the umbrella of significant figures.
Any zeros between two non-zero digits are significant
When you talk about the second principle, students are expected to have slightly more understanding. A lot of them do get confused when it comes to treating zeroes as significant or non-zero figures. If you do not have a strong understanding of the concepts, it would be hard for you to get the correct answers.
In accordance with this rule, if a zero is present between two significant figures, it is counted as significant as well.
We can go through an example to gain more understanding. Consider that you have the numbers “2801” and “56.02”.
If you have a look at both these numbers, you would figure out that there is one thing common. In both these numbers, there is a zero between two significant figures. However, the first number is a whole number while the second has a decimal. This actually does not make any difference. In both these numbers, as the 0 appears between two significant non-zero numbers, there would be four significant digits.
Although this rule is quite simple but still, a lot of students get confused when they are going through it. For instance, when you talk about the number “366020”, there will be five significant figures and not 6. The first zero would be a significant digit because it appears between 6 and 2. However, when you talk about the second which is actually the last digit, it has 2 on the left but there is no significant digit on the right so it would not be counted as a significant figure. Knowing about these regulations is important if you want to avoid errors.
In a decimal number, the trailing zeros are significant
This is actually a tricky regulation and most people find it hard to understand it. When you talk about trailing zeros, they appear after a significant digit. Zeros that appear before the significant digit are not considered trailing so they are not counted as significant figures. We can gain more understanding through an example.
Consider that you have the number 0.0052050
If you have a close look at this number given above, you would realize that there are two zeros before the first 5 and one zero after the second 5. In accordance with the regulation, as the first two zeroes after the decimal do not appear after a significant figure, they would not be counted as significant. However, the last zero which occurs after the second 5 is a trailing zero as it is present after a significant figure.
If you talk about determining significant figures without making mistakes, it is not a very hard task to accomplish. The key requirement is that you would be well aware of the regulations and rules. People who understand these rules with complete clarity do not face any issues. The confusion is only created when people do not have a proper understanding about the regulations.