Mastering the Significance- A Comprehensive Guide to Adding and Subtracting Significant Figures Rules

What is the rule when adding and subtracting significant figures?

When performing mathematical operations, such as addition and subtraction, it is essential to understand the rules for handling significant figures. Significant figures are a way to express the precision of a measurement or calculation. These rules help ensure that the final result reflects the accuracy of the original data.

Rules for Adding and Subtracting Significant Figures

1. Identify the Least Precise Value: When adding or subtracting numbers, the result should be rounded to the same number of decimal places as the least precise value in the calculation. The least precise value is the one with the fewest decimal places.

2. Perform the Operation: Add or subtract the numbers as you normally would.

3. Round the Result: Once you have obtained the result, round it to the same number of decimal places as the least precise value.

For example, if you are adding 2.35 and 0.012, you would round the result to two decimal places since 0.012 has only two decimal places. The calculation would be 2.35 + 0.012 = 2.37, which is then rounded to 2.4.

Subtraction Rules

When subtracting numbers, the same rules apply. The result should be rounded to the same number of decimal places as the least precise value. This ensures that the result is not more precise than the original data.

For instance, if you are subtracting 0.012 from 2.35, you would again round the result to two decimal places. The calculation would be 2.35 – 0.012 = 2.338, which is then rounded to 2.3.

Consider Zeroes

It is important to note that zeroes can sometimes be significant or insignificant in a number. In the case of addition and subtraction, zeroes to the right of the decimal point are always significant. However, zeroes before the first non-zero digit are not considered significant.

For example, in the number 0.012, the zeroes before the 1 are not significant, but the zeroes after the decimal point are significant. Therefore, when performing operations with this number, you must consider the significant figures in the zeroes.

Conclusion

Understanding the rules for adding and subtracting significant figures is crucial for maintaining the accuracy of mathematical calculations. By following these guidelines, you can ensure that your results are as precise as the original data you worked with. Always remember to identify the least precise value, perform the operation, and round the result accordingly.