Rounding Off of 5

[Brandon Mo 4K]

During one of the peer learning sessions, the UA talked about how you were supposed to round to an even number when there is 5. I do not remember clearly what the UA said. But if you were rounding 4.45 to two significant figures, it would be 4.4, not 4.5.

Will we need to do this for future exams (rounding to an even number when rounding off from a 5)?

[Mukil_Pari_2I]

This is just a general rule of sig figs that we must use I believe. A lot of the documents on the website do indicate that we should round to the nearest even number. This is because we will be less precise if we just round up (we would overestimate) and if we just round down (we would underestimate). However, if we round up at times and round down at times for rounding with 5, the average will balance out over time and thus we are more likely to be on average more precise. But yeah, probably just use the rule bc its what the docs regarding sig figs on the chem website say.

[Peichung Chou 1A]

According to the file professor Lavelle posted on his website, you round up to the next number only if there is a number following the 5 (e.g. 4.56 to 2 sig figs is 4.6). Otherwise you round to the nearest even number.

[Saima Salam 3J]

It depends on how many significant numbers the problem is asking for but in this case, 4.45 would be rounded to 4.5 because if you are just rounding to 4.4 it means you are rounding down which is incorrect. The .05 makes a difference in the answer so we can't disregard it by rounding down so the best option is just to round it up to the next number.

[Emily Li 4A]

On Lavelle's site, there is a handy cheat sheet for sig figs if you're ever confused about them. They're under the Math Assistance section in "everything you want to know about significant figures" and "More Significant Figure Discussion". It covers everything in depth, including this topic.

[Jessica Pham_4B]

What you're saying I think is right 4.45 rounded is 4.4. Cause when the number end in 5 you round to the even number. This is what it said on Lavelle's cheat sheet:

IF LAST DIGIT IS ABOVE 5: ROUND UP (2 sf then 2.36 is 2.4)
• IF LAST DIGIT IS BELOW 5: ROUND DOWN (1sf then 2.36 is 2)
• IF LAST DIGIT IS 5: ROUND TO NEAREST EVEN NUMBER
(2 sf then 2.35 is 2.4 and 2.65 is 2.6)
Note: Round to the nearest even digit if there is nothing after the 5,
but round up if there are digits after the 5. For example if we round to
2 significant figures: 2.451 x 102
, the answer is 2.5 x 102 since 2.451 x
102 is closer to 2.5 x 102 than 2.4 x 102

[Andre_Galenchik_2L]

Sorry I am still confused about this rule. For single problems is it not fine to just round up at 5 as it is in the upper half of 0-9?

[505194972 3k]

In most cases rounding up from .5 is not precise enough and you often have to multiply by a value to make it a whole number, specifically when doing empirical/molecular formulas.