Significant Figures: Definition, Usage and Examples

"What are Significant Figures?", "What are they used for?", "What is their significance?"

Students often ask these questions because why would you want to identify significant numbers, if you can do mathematical calculations without them, right?

Where the idea of using significant figures might come off as unnecessary, it is a crucial concept that you need to learn if you want to improve the accuracy and preciseness of your mathematical calculations using measurements.

If you have questions and confusion about significant figures, and you want to know their importance, then you are at the right place. 

In this article, we are going to walk you through the basic concepts behind significant figures, along with their prominent applications that you need to know.

What are Significant Figures?

lots of numbers

When it comes to performing different calculations based on measurements, you only need to use the Significant or the Meaningful Digits from the value. 

This approach allows you to declutter a value and only use the numbers that have meaning and impact on the find result. 

And this is the primary idea behind significant numbers. 

At the most basic level, significant figures are significant and important digits in a value that help you convey the results of that value, without using all the terms written in it. 

You get precise and accurate measurements through this process that you can use to get consistent and accurate results. 

In most cases, the leading or trailing zeros in a standard or a decimal point value are considered to be non-significant. 

Mathematicians have created a certain set of rules that regulate the identification of Significant Digits. These rules define certain conditions that allow you to find Significant Digits quickly and easily in value. 

What is the Significance of Significant Figures in Mathematical Calculations?

Now that you know what significant digits are, you might be wondering why you need to find them?

The applications of Significant Figures become clear when you have to deal with calculations that require an extreme level of accuracy and precision. 

If you are working with long values like the decimal value terms with a lot of digits after the decimal point, using all those numbers just doesn’t make sense. 

You can skip some of those numbers and use only the ones that are significant to find accurate results. 

So, if you want to tidy up your measurements, Significant Figures are a great way to do that. 

Along with that, the importance of Significant Numbers is even greater when we are concerned with the fact that how accurate and precise our results are.

Rules for Counting Significant Digits

  • All non-zero digits and any zeros contained between non-zero digits count.
    500079 = 6 significant digits
  • Leading zeros don't count.
    0.000012 = 2 significant digits
  • Trailing zeros count if there is a decimal point.
    0.0001200 = 4 significant digits
  • Trailing zeros may or may not count if there is no decimal point, so we go with the most conservative answer to not count the trailing zeroes.
    120000 = 2 significant digits as it can be written as $1.2 \times 10 ^5$

Here's the summary:

  1. Nonzero numbers - Always Significant
  2. Captured zeros - Always Significant
  3. Leading zeros - Never Significant
  4. Trailing zeros - Only with a decimal

Applications of Significant Figures

Accuracy and Precision are considered to be the 2 most basic and well-known applications of Significant figures. Using the concept of Significant Figures, you can make sure that the values you are using in various calculations are precise and accurate. 

Let’s go over both these concepts to get a better idea of what we are talking about

Precision of a Measurement

We’ll start by defining the meaning of precision in calculations. Precision is about how close 2 measurements are when placed under the same set of conditions. 

When you find significant figures in a value and use them in the place of the original value, they give you a result that is almost close to the original value. 

This is what makes Significant Figures remarkable as they enable you to declutter the measurements and still generate the same results that you are interested in.

Accuracy of a Measurement 

Once you have found the significant figures, the closeness of those figures with the actual number is referred to as accuracy. 

If two numbers are accurate, you can use them for any calculations and they will give you the same results, under all cases. 

So, if you want to get error-free or accurate results, the use of Significant Figures can help you with that. 

When working with different calculations, you often find numbers that are precise but not accurate. You need to be able to identify them if you don’t want to get inaccurate results. 

Whether you are doing mathematical or engineering calculations, you need to be careful with your approach and consider the significant figures if you want to get accurate and precise results.   

Rounding Significant Figures 

There are various cases where you might need to round Significant Figures to make the calculations simpler for yourself. 

For rounding, you need to select a number that you want to round. After that, you need to consider the number following your selected number. 

If the following number is less than 5, you leave the numbers after your selected digit and the resulting set of numbers is your rounded result. 

If the following number is greater than 5, you add 1 to your selected number and then leave the numbers following your selected numbers. The numbers that you get with us will be the result of the rounding process. 

Calculating Significant Figures – Best Method for Students

When it comes to finding Significant Figures, students have to keep in mind a lot of rules and regulations. 

If you don’t want to use the conventional approach, you can use a SigFig calculator to instantly find the Significant Figures in a value. 

Here is how the Sig Fig calculator works:

  • You need to enter the number in the calculator 
  • Select a round value that you prefer
  • Hit the Calculate button and the calculator will find the significant figures for you 

Additionally, the significant figures calculator gives you the total number of decimals, the E-Notation, and the Scientific Notation of the Input Values as well. 

Significant Figures Calculator

End Notes

What are significant figures?

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and any zeros in the decimal portion.

Why are significant figures important?

They are crucial for accurately representing the precision of measurements and ensuring consistency in calculations.

How are significant figures used in mathematics?

In mathematics, significant figures are used to maintain precision during calculations and to express the reliability of a particular measurement.

How do I determine the number of significant figures in a given number?

Start from the left, count the first non-zero digit and all digits to its right.

What is the rule for addition and subtraction with significant figures?

When adding or subtracting, the result should have the same number of decimal places as the number with the least decimal places.

What is the rule for multiplication and division with significant figures?

The result should have the same number of significant figures as the number with the least significant figures.

How do zeros affect significant figures?

Zeros between significant figures are significant, zeros to the left of all the non-zero digits are not significant, and zeros to the right of all non-zero digits and to the right of the decimal point are significant.

The importance of significant figures becomes apparent when you consider the precision and accuracy of the measurements. You can’t get reliable results with these 2 most important factors. 

And that is exactly where the Significant Figures get you to. Using significant figures, you can make your measurements as neat and as accurate as possible. 

This is all there is to it! If you have any questions about Significant Figures, then get in touch with us. We’d be happy to help you out with your confusion regarding the concept of Significant Figures.