Mathematical calculations require extreme accuracy and precision. When you are engaged in solving mathematical problems, you need to use accurate measurements if you want the process to be as error-free as possible.
And when we talk about accuracy and precision, the discussion is incomplete without Significant Figures.
You need to determine the significant figures in the values that you want to perform the calculation on, and you need to use them to get accurate results. If you don’t have a clear idea about Significant figures and you want to learn about ways to identify them, then you are at the right place.
Let’s take a deep dive into the concept of Significant Figures and go over some of the ways you can identify them quickly and easily.
How to Identify Significant Figures – Tips for Mathematics Students
Tip 1 – All Non-Zero Digits Are Significant
When the value that you want to work with has only the non-zero digits, then all of these zeros would be considered significant.
So, if you get a term that only has numbers other than zero, whether it is decimal or a standard term, you can count the number of digits in it and that would give you the total number of significant digits in that term.
For example, the terms 7683 and 78.635 have 4 and 5 significant digits respectively.
Tip 2 – All zeros Between two Non-Zero Digits Are Significant
When the value that you are working with has zeros enclosed between 2 non-zero digits, then the enclosed zeros would also be significant.
This statement is true whether the value is standard or the one with a decimal point. Consider the example of the number 345.9003. This value has 7 significant figures. The zeros between 9 and 3 are significant in this value. This approach stays true for all similar cases.
Tip 3 – Zeros to the Right of the Decimal Point and Left of the Non-Zero Digits are Insignificant
Values that have zeros on the right of the decimal point and the same zeros comes on the left of the non-zero number in the value, then all those zeros would be insignificant.
To understand this concept better, consider the value 0.00562. This value has 2 zeros on the right of the decimal point and on the left of 5 which is the non-zero digit of the value.
Now, the zeros before 5 in this case are insignificant. As a result that, the term only has 3 significant digits which are 5, 6, and 2.
Tip 4 – Zeros Placed On the Right of the Decimal Point That Is Not Followed by Non-Zero Digits are Significant
If zeros in a decimal point value appear on the right side of the decimal point and they don’t have a non-zero number after them, then those zeros would be significant.
For example, consider the number 789.000. The term has 3 zeros after the decimal point. These 3 zeros are significant.
So, when we calculate the total number of significant figures in the value, the answer for that would be 6.
The thing to keep in mind here is that the zeros after the decimal point should not have a non-zero number following them. If this condition holds true, you can simply just count the total number of significant numbers in that value.
Tip 5 – Zeros that Appear on the Right of the Last Non-Zero Digits After the Decimal Point Are Significant
This tip is kind of like the extension of what we have talked about in tip 3. If there are zeros in a decimal point value that appear to the right of the last non-zero digit in that value, then those zeros would be considered significant.
Let’s take the value 0.00983900 as an example.
This value has 2 zeros on the right of the last non-zero number in the value which is 9. So, the 2 zeros will also be significant.
So, the total number of significant numbers in this value would be 6.
Tip 6 – Zeros Placed on the Right of the Non-Zero Digit Are Significant If They Are a Part of a Measurement
Whether you are working with a standard number or one that has a decimal point, if that number has been calculated as part of a measurement, then the zeros in it would be significant.
For example, let’s say you have calculated a value which is 780 m. Now, in a general case, the last zero after 8 would have been insignificant. But since the number is a part of the measurement, we must consider the zero in it as significant too. So, the term 780 m has 3 significant digits in this case.
Bonus Tip – Use the Sig Fig Calculator to Easily Identify the Significant Figures
All the tips that we have talked about in this article are based on the rules for identifying significant figures. If you use this approach, you have to memorize all these tips and use them at the right time to get the results that you want.
But there is an easier way of finding Significant Numbers. And that is by using the significant figures calculator.
Sig Fig Calculator is a free tool that you can use to find the total number of significant figures in a value, without doing any kind of manual calculation.
Here is how you can use our Sig Fig calculator:
- Enter the value that you want to find the number of significant figures in
- Select your preferred round value
- Click on the Calculate button on the Sig Fig calculator
The calculator will give you the total number of significant figures, decimal numbers, the E-Notation, and the Scientific Notation for your input number.
Wrapping Up
Significant Figures are of critical importance when it comes to doing accurate mathematical or engineering calculations. You can’t afford to use measurements that are even just a little bit of. If you don’t want to use the wrong measurements and you want to make sure that you use correct values all the time, you need to learn how to identify the significant figures.
Go over the methods for Significant Figure identification that we have talked about here. And if you have questions about Significant Figures, feel free to reach out to us.