When it comes to doing any kind of calculation, precise and accurate measurement is all that matters. Mathematicians and scientists are always trying to come up with a robust set of principles to minimize the errors in measurements and to find out the best possible representation of numbers. In the way to making scientific measurements accurate and error-free, the role of significant digits is of utmost importance.
In this article, we are going to take a deep dive into significant numbers and talk about some rules and examples about significant numbers that will help you understand the concept in greater depth.
What are Significant Figures?
Significant figures are numbers that represent the meaningfulness of a number and also represent its precision.
In simpler terms, significant figures or digits are important numbers in a given value that are a must to accurately convey the message that a value is supposed to represent.
For example, the term 123.45 has 5 significant digits. The significant figures range from 0 to 9 and are generally the coefficient of the given expression.
Significant Figures help scientists and engineers streamline the accuracy of various measurements. The system of determining significant figures greatly reduces the chance of making errors when doing different calculations.
Why Determine Significant Figures?
Significant Figures help scientists, engineers, and mathematicians narrow down a number in terms of the digits in it that are of significant importance. There are many reasons why you would want to figure out the significant figures. Precision and Accuracy are two of them.
Precision is about the closeness between two or more quantities when they are placed under the same conditions. When you determine the significant figures, the resulting numbers give you the same results in measurements as the original number. This enables you to discard the numbers in a measurement that don’t need because they have the least importance.
Accuracy is another important factor that makes the significant figure calculation useful. It is the closeness between the significant figures and the actual number. Using the principles of accuracy, you can generate consistent results.
Significant Figures Rules
If you want to determine the significant figures in a given set of measurements, you need to follow certain principles. These principles are quite straightforward to understand.
Still, if you want an easier approach, you can use the sig figs calculator to automatically determine the significant figures in a value.
Here are the rules that you need to follow when calculating significant figures:
- All the non-zero numbers in a value are significant. For example, the number 56735 has 5 significant figures.
- If the zeros in a value occur between two non-zero digits, then all those zeros are significant. For example, the number 3002.1023 has 8 significant figures.
- If a zero appears on the right of a decimal point and they are on the left of a non-zero digit are not significant. For example, in the term 0.0056, there are only 2 significant figures.
- All zeros on the right side of a decimal point would be significant if they are not followed by a non-zero digit. For example, in the term 20.00, there are 4 significant figures.
- All the zeros that are on the right side of the last non-zero digit and come after the decimal point are significant. For example, the term 0.0098700 has 5 significant figures.
- All the zeros that are on the right side of the last non-zero digit will be significant If they are a part of a measurement. For example, the term 109cm has 3 significant figures.
How to Round the Significant Figures?
To get accurate measurements, you can also round a number off. You need to leave a digit from the right to do that. The rounding-off process is also quite simple and follows a certain set of rules.
Let’s go over the principles that you need to follow when you have to round some significant figures.
- First, you need to determine the digit on which you want to perform the rounding on. When rounding off numbers, if you find a digit that is less than five, you need to leave all the numbers that are remaining on the right side.
- Now, if the digit next to the rounding off digit is greater than 5, then you need to add 1 to the digit that you want to round off and then exclude all the other digits on the right side.
For example, let’s try rounding off the number 54.3671.
Now, if when had to round it to 3 digits, we’d look at the last number and since it is 1, we can just leave it according to the first rule.
So, the resulting term would be 54.367.
Now, if we want to round the number to 2 digits, we need to look at 7. And since 7 is greater than 5, we need to add 1 to the number that is before 7. The 6 would become 7 and the result would be 54.37.
Examples of Significant Figures
Let’s take a look at some examples and try to identify the significant figures in them.
Example #1:
4567
There are 4 significant figures including 4, 5, 6, and 7 in this value.
Example #2:
7.26520
There are 6 significant figures including 7, 2, 6, 5, 2, and 0 in this value.
Example #3:
0.0523
There are 3 significant figures in this value.
You can try more values to get a better grip on the concept. Simply just memorize the rules for finding significant figures and then keep applying them to the values that you have to process.
Final Words
Significant numbers indicate the precision and accuracy of given measurements. These numbers indicate the digits in a measurement that are significant so that you can safely discard the ones that don’t have any kind of impact on the overall value.
You can use the above rules and examples to determine significant numbers in a measurement. The online Sig Fig calculator can also be used for this purpose.