Introduction to Significant Figures: Explained with Definition, Rules, & Examples
Scientists all over the world agree that mathematics is the language of the universe. They argue that if we wish to understand the reality of things at the deepest level, mathematics is the pathway to get to that.
Whether you are interested in physics, chemistry, or any other branch of science, you have to use mathematics to prove the theories that you come up with.
If the mathematics supports your hypothesis, then you can say that the conclusions that you have arrived at are true.
And the trueness of mathematical calculations relies heavily on the accuracy and precision of the measurements that we base our calculations on.
How can we make sure that our mathematical calculations are precise and accurate?
This is where the role of significant figures comes into play.
So, what are significant figures?
Significant Figures are an integral part of basic as well as advanced mathematical calculations where being accurate and precise is your primary concern.
In this article, we are going to go deep into the details of significant figures and how they factor in with mathematics.
So, without further ado, let’s get started and talk about the importance of significant figures in mathematics along with few examples.
How do you calculate significant figures?
Before moving towards examples, you should know how to calculate them. There are two ways to calculate significant figures.
Exmaple – Sig Fig
Find sig figs in 0.03302.
The following rules will be applied to the above number.
All decimal are significant number except leading zero ignored.
Leading zeros in a number are always ignored to be significant.
So, there are total of 4 significant figures in the decimal 0.03302.
No. of significant figures are: 4
Significant figures: 3, 3, 0, and 2.
You can use sig fig calculator to find the significant figures in any number, i.e., whole number, decimal, etc.
Rules to find significant figures
- To perform manual calculations, you have to follow these significant figures rules:
- The numbers without any zero digits are all significant whether they are whole numbers or decimals.
- A zero between non-zero digits is significant.
- A zero at the extreme right of a decimal point is significant.
- A zero at the extreme right of a whole number is not significant.
- Starting zeros are not significant.
Significance of Significant Figures in Mathematics
The importance of significant figures in mathematics is undeniable. They tell how accurate a measurement is as compared with the original one, under the same conditions.
Here are some of the most prominent reasons why finding Significant Figures is essential in Mathematics
- Understanding the Universe with Maximum Accuracy
We have already established that mathematics is the gateway through which we can understand the reality of the universe.
But we need to be extremely accurate when doing that. Because if use wrong measurements, then the principles and results that we infer from it would also be inaccurate.
Significant Figures help you identify whether the measurement is accurate or not. You can use accurate measurement to get consistent results that comply with the standards set by the original value.
When you find accurate measurements, they minimize the possibility of errors in your mathematical calculations.
- Precision in Understanding and Utilizing Different Measurements
Accuracy is not the only factor that you need to consider when doing the calculation in mathematics. You also need to consider the preciseness of the values.
Preciseness shows how close the values are when they are placed and processed under the same conditions.
Understand the preciseness of a value helps you derive the same results as the original value, with utmost precision.
When you use precise measurements, it adds accuracy to your calculations. You can feel confident that the calculations you are doing are delivering you the kind of results that you want.
- Rounding a Value
When working on mathematical problems, you are often required to round a value during the calculations or when representing your answers.
The whole concept of rounding different values relies on the principles of significant figures.
The rounding happens around the significant figures in a measurement. The way you do it is by identifying the number where you want the rounding to happen.
After that, you use the rounding principles where you add 1 to the number you want to round or keep it the same based on whether the number after that is greater than or less than 5.
- Tidying Up Calculations
When you are working with different values in mathematics, you sometimes have to deal with decimal point values that have a lot of digits in them. For example, let’s say you have a value such as 12.53564000.
Now, using this value in every calculation is going to be a lot of hassle for you.
This is where the role of significant figures becomes important. You can identify the digits in the value that are of most importance.
After that, you can use those values and skip the rest. You can use either significant figure principles or the rounding rules here to narrow down and tidy up the given term.
- Coming Up with Scientific Notation of a Value
When you express a number as its scientific notation representation, you do it around the significant digits in that number.
You identify the significant digits in the value, and you use that information to express a number in the form of its scientific notation.
So, whenever you are dealing with numbers that you need to represent in the scientific notation format, you need to take help from the principles of scientific figures.
You need to find significant figures and then use them to convert a number to its scientific notation form.
Figuring out significant figures is incredibly essential for doing a correct mathematical calculation. If you rely on the conventional means of calculation, you never know how accurate you are being there.
So, if you want to maximize your accuracy and preciseness when doing mathematical calculations on numbers, we recommend you use significant figures instead.