Rounding to the appropriate number of significant figures helps convey the limitations of our measurements while maintaining accuracy.

Let’s explore how to round a value to a given number of significant figures in a clear yet comprehensive manner. We’ll do that in explanatory steps. (A significant number calculator would be easier)

• The first step is to identify the last significant digit – the digit in the place furthest from the decimal point that is known with certainty. For example, in the number 234.5678, the last significant digit is 8. 
• Next, examine the digit immediately following the last significant digit. 
• If this digit is less than 5, we simply drop it and any digits further right. “Drop” means turn to zero. So 234.5678 rounded to 3 significant figures would be 234.0000, which is the same as 234. 
• In the case where the following digit is 5 or greater, we round the last significant digit up by 1 and discard the digits after. So 234.4548 rounded to 3 significant figures would be 235. 

Let’s look at a few examples to cement our understanding. 

• 0.00328 rounded to 4 significant figures is 0.00328 as the last three digits are all significant. 0.00328 rounded to 3 significant figures becomes 0.003. Moving the decimal point right, 3245.91 rounded to 2 significant figures is 3300 as the last digits before the second significant figure, 45, will get rounded up to 1, which will be added to 2 to make 3300. 

How to Perform The Basic Math Operations With Numbers Having Different Significant Figures

Addition and Subtraction: 

When adding or subtracting terms, the final answer needs to match the original value with the lowest amount of significant figures. For instance, if you added 12.34 and 5.6 together, you’d round the total to two significant figures to align with the 5.6. So that would be 17.94 rounded to 17.9

Multiplication:

In multiplication, aim to carry over the same degree of accuracy as the factor containing the fewest digits. Take 12.34 multiplied by 5.6 – the product would be expressed as 69 to two significant figures.

Division: 

For division, the quotient takes on the significant figure count of the number you’re dividing by. Dividing 12.34 by 5.6 would yield approximately 2.2 rounded to two significant figures, in keeping with the 5.6.

Just as a heads up, there are 2 basic rules to follow when performing arithmetic operations that involve decimals.

The basic rules for determining the number of significant figures in the final answer of an arithmetic operation are:

• For addition and subtraction, the final answer should have the same number of decimal places as the number with the least number of decimal places in the operation.
• For multiplication and division, the final answer should have the same number of significant figures as the number with the least number of significant figures in the operation.

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Conclusion

It’s easy to forget these guidelines, especially when using a calculator. Be sure to double-check that any automated solutions are properly truncated. And remember – the end result can only be as exact as the least exact original value. Following these norms helps communicate the limitations imposed by measurement variability in quantitative analysis.