Many students find significant figures confusing when they first see them. They understand the formula, but their final answer is marked wrong because of extra or missing digits. They apply significant figure rules the wrong way.
In fact, basic calculation and rounding errors are one of the most reported mistakes in early science and math courses. In this blog, we will explain what significant figures are in simple words. We will cover the basic rules and show how to count and use them in calculations. We will also give clear examples so beginners can understand and apply them correctly.
What are Significant Figures?
Significant figures are the digits in a number that carry meaning about its precision. These digits tell us how accurate a measured value is. They include all certain digits and one estimated digit at the end.
For example, when you measure a length using a ruler, you may be sure about some digits, but the last digit is usually an estimate.
In science and engineering, significant figures indicate the accuracy of measurements. They prevent us from writing numbers that look more accurate than the actual measurement. That is why significant figures are used when reporting measurements and calculation results.
What Are the Rules to Calculate Significant Figures?
To calculate significant figures correctly, you need to follow a few basic rules. These rules apply to most numbers used in math and science. You can also practice and master significant figures with examples to strengthen your understanding.
Rule 1
All non-zero digits are significant. Any digit from 1 to 9 is always counted as a significant figure. For example, the number 347 has three significant figures.
Rule 2
Zeros between non-zero digits are significant. If a zero is placed between two non-zero digits, it is counted. For example, 405 has three significant figures.
Rule 3
Leading zeros are not significant. Zeros that appear before the first non-zero digit are not counted. For example, 0.0062 has two significant figures.
Rule 4
Trailing zeros in a decimal number are significant. If a number has a decimal point, the zeros at the end are counted. For example, 2.50 has three significant figures.
Rule 5
Trailing zeros in a whole number may not be significant. If there is no decimal point, trailing zeros can be unclear. For example, 15000 may have two, three, four, or five significant figures depending on how it is written. This confusion can be solved by writing the numbers in scientific notation.
Rule 6
Exact numbers, such as defined conversion factors, have infinite significant figures. Constants like π are treated as exact unless they are rounded for calculation purposes.
Rule 7
To determine the significant figures in the values written in scientific notation, like X × 10x, the rules will only apply to the “X”. The superscript on the “10x” is considered an exact number. So it contains an infinite number of significant figures. Like:
1.5 × 103 contains 2 significant figures.
1.50 × 103 contains 3 significant figures.
1.500 × 103 contains 4 significant figures.
1.5000 × 103 contains 5 significant figures.
How to Calculate Significant Figures?
Now, when we have a clear understanding of the rules of significant figures, we will look into the step by step process of finding the number of significant figures. We will use “0.00450780” as an example. Here is the process:
Find the First Non-Zero Digit
The zeros before the first non zero digit are useless. The first non-zero digit in our example is 4. This is where counting of significant figures starts.
Count All Digits After the First Non-Zero Digit
Now, when you have found the initial non zero digits, count all the other digits. This must include all the other zeros that may be between or at the end of non zero digits.
Count the Total Significant Figures
Now, list all the significant digits:
4, 5, 0, 7, 8, 0
That makes a total of six significant figures. So the number 0.00450780 has 6 significant figures.
After learning the rules and practicing them, most students start feeling more comfortable with significant figures. Still, mistakes can happen, especially when dealing with zeros and rounding. In such cases, students can take help from Sig Fig Calculator to double-check their work. It can count the accurate significant figures in a value. You can compare your answers and find out if your findings are correct or not.
Calculations With The Significant Figures
When doing calculations with measured values, the first thing you should check is how many significant figures each value has using the above mentioned rules.
When we add or subtract two or more than two measured values, the position of the decimal should be matched to the value with the fewest number of decimal places. This value is called the limiting value.
For instance, if we add 43.01 and 73.595, then the limiting value here is 43.01, which has only two decimal places. That is why the addition result will have two decimal places only.
On the other hand, the rules are different for multiplication or division. Here, the overall number of important figures counts rather than decimal locations. The final result should have the same number of significant figures as the number with the fewest significant digits.
For example, when multiplying 2.445 and 31.7, 2.445 has four significant figures, whereas 31.7 only has three. As a result, three meaningful digits should be recorded for the final calculated value.
Final Words
The significant figures are important digits, as they tell us about the accuracy of the numbers. If you do not find them in a value, you cannot get the right answers, no matter if your formula or other procedure is correct. That is why students lose marks in math and science exams. By following the basic rules for counting significant figures and applying the correct method in calculations, you can avoid these common mistakes. Always check whether the question needs decimal place rules or total significant figure rules. With time and regular practice, these steps become easier.
