About rounding off for significant figures

[shortydeb]

Let's say I want to round the number 3.549 off to two significant figures. Do I have to round the 4 to 5 first, or do I just round the 5 (in the one-tenths place) to 5, since the one-hundreths digit is 4? If I do it by the first method, it would be 3.6, while the 2nd method gives 3.5. Which is right?

Thanks.

 

[Defennder]

It should be 3.5. You look at the digit which is one-tenth the value of the previous one on the left. The significant values should be the digits in the largest tens/tenth places, and then you round up/down the digit which are next to it.

 

[Moetasim]

Hello,

Thank you for your question about rounding off for significant figures. As a scientist, it is important to understand the rules for rounding off numbers to maintain accuracy and precision in our calculations and measurements.

When rounding off to two significant figures, the first method you mentioned would be the correct approach. According to the rules for significant figures, the first non-zero digit and all subsequent digits are considered significant. In this case, 3.549 has four significant figures, so when rounding off to two significant figures, we must round to the first two non-zero digits.

Therefore, we would round the 4 in the one-tenths place to 5, resulting in 3.6. This is because the 5 in the one-hundredths place is not significant in this case, as it is preceded by a zero.

The second method you mentioned, rounding only the 5 in the one-hundredths place to 5, would result in 3.5. However, this would not be the correct approach for rounding to two significant figures.

In summary, when rounding to two significant figures, we must consider all non-zero digits in the number and round to the appropriate digit based on the rules for significant figures. I hope this helps clarify the correct method for rounding off to significant figures. If you have any further questions, please let me know.

Best regards,