How to Add and Subtract with Significant Figures
In scientific calculations, the accuracy of the results depends not only on the precision of the measurements but also on the proper handling of significant figures. Significant figures are a way to express the precision of a number, and they play a crucial role in addition and subtraction operations. This article will guide you on how to add and subtract with significant figures correctly.
Understanding Significant Figures
Significant figures are digits in a number that carry meaning in terms of precision. They include all the digits that are known with certainty, plus one uncertain digit. For example, in the number 123.4, there are five significant figures: 1, 2, 3, 4, and the last digit, which is uncertain.
Rules for Adding and Subtracting with Significant Figures
When adding or subtracting numbers with significant figures, follow these rules:
1. Identify the number with the least number of decimal places. This number will determine the number of decimal places in the final answer.
2. Perform the addition or subtraction operation as usual.
3. Round the final answer to the same number of decimal places as the number with the least number of decimal places.
Example 1: Adding Significant Figures
Let’s add the following numbers: 2.34, 1.23, and 0.78.
1. The number with the least number of decimal places is 0.78, which has two decimal places.
2. Add the numbers: 2.34 + 1.23 + 0.78 = 4.35.
3. Round the final answer to two decimal places: 4.35.
So, the sum of 2.34, 1.23, and 0.78 is 4.35.
Example 2: Subtracting Significant Figures
Now, let’s subtract the following numbers: 5.234, 2.34, and 0.78.
1. The number with the least number of decimal places is 0.78, which has two decimal places.
2. Subtract the numbers: 5.234 – 2.34 – 0.78 = 2.12.
3. Round the final answer to two decimal places: 2.12.
Therefore, the difference between 5.234, 2.34, and 0.78 is 2.12.
Conclusion
Adding and subtracting with significant figures is an essential skill in scientific calculations. By following the rules and rounding the final answer correctly, you can ensure the accuracy of your results. Always remember to consider the number with the least number of decimal places when performing these operations.
