## Rounding to 1 sig fig when there is a 5

Chem_Mod
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### Rounding to 1 sig fig when there is a 5

Question: Let's say you are to round to 1 significant figure and your answer is 0.458. Would your answer become 0.4 because the 5 rounds down to the nearest even number? Or would it round to 0.5 because the 8 rounds the 5 to 6, which rounds the 4 to 5. In essence ... how many "extra" numbers should we be carrying over in a problem? Do we "cut" off numbers to the right of one "extra" number?

Chem_Mod
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### Re: Rounding to 1 sig fig when there is a 5

Answer: When rounding a number like 0.458 to one sig fig, you only take into account the very next number. Everything after that is irrelevant. So in this case, the 5 determines how to round and the 8 is not considered at all.

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### Re: Rounding to 1 sig fig when there is a 5

In the chem 14A workbook, it says that you should round the number up if there are digits after the 5. "For example, if we round to 2 significant figures: 2.451 * 10^2, the answer is 2.5 * 10^2 since 2.451 * 10^2 is closer to 2.5 * 10^2 than 2.4*10^2" This is quoted from the workbook. So I'm confused if we should consider the digits after the 5 when deciding to round. Also, if we do consider the digits after the 5, would 0 count as a digit that would make the number be rounded up?

Regina Chi 2K
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### Re: Rounding to 1 sig fig when there is a 5

Hi Soraya!

I understand what you mean. The appendix in the back of the textbook says to round to the nearest even number. Despite having 4.45 that would supposedly round to 4.5 (given the fact that the problem only wants two significant figures), the the book says that it should be rounded to 4.4 according to their rules. However, I am pretty sure that all problems have answers by rounding to the next higher digit if the digit you are considering is "5" or higher and rounding to the previous digit if it is "4" or lower. And you do not consider the digit after the five when rounding to the next digit! I hope this clears things up and if you have any questions, feel free to ask! :)

Anna Nordstrom 1A
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### Re: Rounding to 1 sig fig when there is a 5

The rounding rules with the number 5 are a little different. You round to the nearest EVEN number. For example, if I have .85 and I am rounding to one sig fig it would round to .8
If I had .35 and I was rounding to one sig fig it would round to .4 because .4 is the nearest even number. In this case it rounds up but in the last case it rounded down.