When working on physics problems, you have to deal with a lot of measurements. You need to process these measurements accurately and precisely, to get to your desired results.
Accuracy and Precision matter a lot when we talk about measurements in physics. Accuracy refers to how close a measurement is to the actual value of the measurement.
Precision tells how close the values repeated under the same conditions, are to one another.
When determining both these factors, the use of significant figures or digits is of great importance. Physics problems often require you to express your answer as the significant digits in that answer.
So, you need to know how to count and identify the significant digits that represent the accuracy of your answer.
In this article, we are going to take a deep dive into significant figures and how to count them for physics problems. So, let’s get started and talk about the method for counting significant figures in physics problems.
Significant Figures in Physics Problems
Physics problems use different kinds of measurements. When dealing with these measurements, using the significant digits can prove to be quite useful.
When you count and identify significant figures in a physics problem, it makes it easier for you to use the number in various calculations.
And when you are done with the calculation, you can present your answer in terms of the significant numbers in it, using the scientific notation approach.
For example, let’s say you have a measurement that is 2.7mm. You can write it a 0.27cm or 0.0027 m. As you can see, only the numbers 2 and 7 are the significant values.
The representations other than 2.7 have a lot of zeros but those are only placeholders for different measurements. 2 and 7 are the basic values that have been calculated in the given measurement.
You can further represent your answers in scientific notations. When you do that, all the numbers that appear are significant.
The Need for Significant Figures in Physics
Physics calculation relies heavily on the accuracy and precision of the measurements under the same conditions. Significant figures in physics help you do just that.
When you have to determine the accuracy and precision of measurement in physics, Significant Figures enable you to get to that. Besides, when you reduce a value to its significant digits, you basically declutter it.
SO, when you have to do the further calculation, you can use only the significant figures of the value and still get the same level of accuracy and precision with your measurement.
Rules for Counting Significant Figures/Digits in Physics
The basic rule is you need to know the values that you have to work with. Those values would be your significant digits.
For example, if you have two significant digits with the value 2.5, then those would be the concerned digits for you, even if the term is 2.53354784.
The terms after 5 don’t have a lot of impact on the calculation.
Another interesting thing to note is when working with numbers in physics, the significant numbers are different from standard numbers and measurements.
For example, the number 56,000 and the measurement 56,000 has a different number of significant digits.
The trailing zeros in the number 56,000 are not significant so it has only 2 significant numbers.
If the number 56,000 was some kind of measurement, then it would be written as is in every case. So, it has 5 significant figures in this case.
Now, let’s dive in a little deeper and talk about the rules for counting significant figures when doing different kinds of mathematical operations in physics.
Multiplication & Division
When you multiply or divide 2 numbers, the result is going to have the same number of significant digits as the smallest number of significant digits in any of the given numbers.
For example, if you divide 20.0 with 8.0, you get 2.5. As you can see, the result has the same number of significant digits as the term with the smallest number of signaling digits i.e., 8.0.
Addition and Subtraction
When adding or subtracting numbers, the least significant digit of the result should correspond to the least significant digit in the measurement that is the least accurate.
This sounds a little bit confusing. So, let’s take an example to understand the rule a little bit better.
Consider the following addition:
6.1 + 13 + 5.67 = 24.77
Since the term 13 doesn’t have a significant digit on the right side of its decimal point, the answer shouldn’t have one either, as per the rule. So, you’d need to round the value to 25.
These are the basic rules that you need to keep in mind when working with measurements in physics. But still, it requires you to count significant figures. So, you need to know how to identify them in a physics measurement.
How to Count Significant Figures in Physics Easily?
Before working with measurements in physics, you need to know the accurate number and representation of significant figures in them.
You can either use the rules for determining significant figures, or you can use the online sig fig calculator to count the total number of significant digits in physics problems.
The use of the sig fig calculator makes the process a whole lot simpler and easier for you.
Using the sig fig calculator, you can add the measurement in the input box and the calculator will tell you the number of significant figures in it.
And to give you the exact details about the significant digits, you are also given the scientific notation of the number that you can use to see what the significant figures actually are in the measurement.
This is it! This is the method that you need to use to count significant figures in physics problems. The process is not complicated, but still, you can get it wrong if you are not careful.
So, if you want to make sure that you count the significant figures accurately every time, we suggest you use the sig-fig calculator. You can use this calculator to identify the significant digits quickly and easily in your physics measurements.