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What are the 5 Rules for Significant Figures?

Sep 21, 2021

Whether we talk about basic or advanced mathematical or engineering problems, we have to deal with significant figures all the time. Significant digits in a value are important digits in that value that can be used to express the value, without losing its meaning.

In simpler terms, these are meaningful numbers that can represent the same message as the original measurement, with utmost precision and accuracy. When we have to write the most accurate and precise form of a quantity, we use the significant figures from the calculation. But how can you calculate the significant figures in a value? What are the best rules that you can use to identify significant figures when you come across them?

This is what we are going to address in this brief guide. We are going to share with you some of the pre-defined rules that you can use to find significant figures in a value. So, without further ado, let’s get started and learn the 5 rules for significant figures 

5 Rules for Significant Figures

Over the years, scientists and mathematicians have come up with a set of rules that enable you to identify significant figures in a value. These rules have been able to hold for a long period of time.

Here are the 5 rules for significant figures that you can use to determine the meaningful digits in a value:

Rule No.1: All non-zero numbers in a value are significant

This rule is applicable on the terms with or without the decimal point. The numbers that are not zero in a value, are always significant.

When talking about significant figures, we consider the numbers that have actually been calculated when doing a measurement. And all the non-zero digits are always the ones that are calculated. You can further round off the value to make it smaller. But the non-zero digits are always going to be significant.

Let’s look at some of the examples of non-zero digits that are significant in a value.

Consider the number 123324. This term has 6 non-zero digits and they are all significant.

For the next example, let’s talk about the number 435.123. Although this term features a decimal point, all 6 digits are significant because they are all non-zero.

You can’t leave any of these numbers out as they all represent a measurement that has been calculated.

Rule No.2If one or more zeros come in between two non-zero digits, then those zeros are significant

When we talk about the standard terms of the ones that have decimal points, if they have zeros appearing in between two non-zero numbers then those zeros would be significant. We are not talking about the trailing zeros or the ones that appear before a number. Those scenarios will be discussed later on.

Consider the example of the number 12.009876. As per the rule, this term has 8 significant digits. All the zeros in this value are significant as they come between 2 numbers.

The rule would’ve been different if the zeros had appeared someplace else in the value. It varies from rule to rule. 

Rule No.3Zeros that appear to the right of the decimal point and the left of the non-zero digits are not significant

This rule has 2 conditions that you need to understand. The first condition is that the zeros that appear to the right of the decimal point are not significant. But this statement is only true if the 2nd condition is true. The 2nd condition states that the zeros should appear to the left of the non-zero digits in the decimal point.

Let’s look at a number to understand this example a little bit better.

Consider the number 0.000876.

If we look at it as per the rule, this number has zeros on the right side of the decimal point and the same zeros appear on the left of the non-zero digits.

We can leave these zeros out. So, the significant digits in this value are 3 which are 8, 7, and 6

Rule No.4Zeros that appear on the right of a decimal point, but don’t have a non-zero digit after them, those zeros are significant

This statement also follows two conditions. If there are only zeros on the right side of the decimal point and the same zeros are not followed by a non-zero number, then those zeros will be significant.

To understand this example better, let’s look at the number 45.00

This value has 4 digits and the 0s on the right side of the decimal point agree with the conditions of the rule. So, all 4 digits of this value would be significant.

Rule No.5Zeros that appear on the right side of the last non-zero digits after the decimal point are considered significant

This rule, although comes off as a bit confusing when you read it, is quite simple in reality. It is a bit like rule 3 but adds to it by saying the zeros that come right after the last non-zero digit in the decimal point term are significant.

Consider the number 0.00763700 to understand this rule better.

As per the conditions of the rule, the 0s on the far right come on the right side of the last non-zero digits in the decimal point. So, those 0s will be considered Significant.

Hence the term 0.00763700 has 6 significant digits.

Best Free Significant Figure Calculator for Hassle-Free Calculation

                Significant Figures Calculator

Learning the rules for finding significant figures is quite important if you want to get a good grip on this concept.

But if you know you are not going to be dealing with significant figures a lot, then you can use the Significant Figures Calculator to get by.

The Sig Fig calculator is a free online calculator that allows you to identify the total number of significant figures, decimal numbers, E notation, and scientific notation of the input value.

Use the Sig Fig calculator to identify significant figures in a value without the hassle of manual calculation.