# Circumstances where rounding by 3 or more decimal places is important

Are there any situations where rounding up by 3 or more decimal places is required?

I have a computer system that is producing rounding errors if it rounds by only 2 decimal places. However, if i choose to round by 3 then the result is accurate.

I cannot however figure out why i need to do this.

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I dont fully understand what you mean; you are asking why 0.312 is more accurate than 0.31? –  CBenni Dec 12 '12 at 18:07
The system i am using asks for how many decimal places to round to. If i choose 2 then calculations are slightly out: by 1 cents in most cases. If i choose 3 then everything is accurate –  Marty Wallace Dec 12 '12 at 18:10
Yes, because if you cut off decimal places, information gets lost. consider $0.413+0.654+0.724$, if we cut off the third digit, we get $1.78$, with our third decimal we get $1,791$ and rounded, that is $1.79$ –  CBenni Dec 12 '12 at 18:13
More places always increases accuracy. Often one guard digit is sufficient, but not always. Think if you have to round 0.04949995 and need to know that it is truly less than 0.0495 so you round down. One simple approach is to keep all the places until the final result, then round and hope for the best. –  Ross Millikan Dec 12 '12 at 18:32

It may be that your program is rounding the terms AND the product. For example, .915 * .335 = .306525 which rounds to .31, but .92 * .34 = .322 which rounds to .32. That would account for the $0.01 rounding error you're experiencing. - I am not exactly sure what you mean, but I recon this is answering your question: For example we want to calculate$0.12*0.34$. the exact solution is$0.0408$, however, rounded to 2 decimal places, it is$0.04\$ which is (obviously) inaccurate.