# Is there an SOP on Rounding Numbers

A

#### Aaron Lupo

I was wondering if any one out there has a SOP on rounding? If you do I would appreciate it if I could get a copy to use as a guide and or model.

Thanks

D

#### Don Watt

Hi ISO GUY,
Please excuse my ignorance (I suspect I'm not the only one though), what do you mean by "rounding"?

A

#### Aaron Lupo

Sorry I should have explained myself. What i was looking for is a procedure on rounding numbers, to make sure that the company is all doing it the same way. For example you have 1.55 and you only need to go out to tenths is it 1.5 or 1.6? I know the people I work with a very intelligent but I was just looking for some guidance on writing a procedure so that we all do it the same.

S

#### Steven Truchon

Interesting topic.
I would think that rounding to whatever the application requires would be the best route. For example, if dealing with mfg tolerances at .xxx but result or measurement data is at .xxxx, round to the third place. It keeps apples with apples so to speak. I have only seen this not be effective when dealing with absolute minimum and maximum limits.
As for things like QS9000 requiring Cpk minimums of 1.33, I would round to two places as the reqs are written, 1.324=1.32 and 1.325=1.33 etc. I realize that the Cpk example is a minimum limit requirement, but we set our software and procedures up to reflect two decimal places and it was acceptable to our registrar, so...
As for your own systems purposes, I suppose selecting the resolution you feel is sufficient to the application and round to that.

A

#### AJPaton

Just to add another log to the fire, our rounding problems come up when we have dies that are fractional rather than metric.

So then we have numbers that can't be rounded.

And when rounding you've got to take GD&T into account, since tolerances add up. (Learnt it the hard way)

AJP

S

#### Steven Truchon

Originally posted by ISO GUY:
For example you have 1.55 and you only need to go out to tenths is it 1.5 or 1.6? I know the people I work with a very intelligent but I was just looking for some guidance on writing a procedure so that we all do it the same.
I just re-read your post and at the risk of sounding too elementary on this, in mathematics, rounding has always been to round down with the last digit being 4 or below and round up if the last digit is 5 or above. 1.04 rounds to 1.0 and 1.05 rounds to 1.1

AJ, yer right on the GDT app, I got bit hard on that one too!

A

#### Al Dyer

I might as well add another log.

In measurement you might need to take the resolution or discrimination ratio of a gage into consideration.

ASD...

G

#### Graeme

Originally posted by ISO GUY:
... What I was looking for is a procedure on rounding numbers, to make sure that the company is all doing it the same way. For example you have 1.55 and you only need to go out to tenths is it 1.5 or 1.6? ... I was just looking for some guidance on writing a procedure so that we all do it the same.
You need to buy a copy of ASTM E29-93a, "Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications". This standard can be purchased as a download or print copy from ASTM ( http://www.astm.org ). The same method is also in ASTM Manual 7, "Presentation of Data and Control Chart Analysis". It also used to be in an old military standard that now appears to be extinct.

Clause 6.4 of E29 covers the rounding rules, which go beyond the 5/4 rule we learned at an early age. Here is a brief summary.
• When the digit beyond the one you want to keep is less than 5, do not change the digit you are keeping.
• When the digit beyond the one you want to keep is greater than 5, increase the digit you are keeping by 1.
• When the digit beyond the one you want to keep is equal to 5 and there are non-zero digits beyond it, increase the digit you are keeping by 1.
• When the digit beyond the one you want to keep is equal to 5 exactly, and the digit you are keeping is odd, increase the digit you are keeping by 1. If the digit you are keeping is even, keep it unchanged.

This method is slightly harder to learn, and it is hardly ever implemented in calculators or computer programs. However, it does reduce the amount of statistical bias that is introduced by the simplistic 5/4 rounding method.

------------------
Graeme C. Payne
ASQ Certified Quality Engineer

R

#### [email protected]

Rounding up or down if the last digit is larger or smaller than 5 has been covered. In a previous life I used to use the rule if the last digit was 5 round the number so that the remaining digit was even. This meant that 1.65 would become 1.6 and 1.75 would become 1.8. For a large column of numbers this would mean some numbers rounded up and some rounded down therefor the total wouldn't be skewed one way or the other and would be closer to the real number. Banks round the direction that would help them and calculator/spreadsheets normally round up when the last digit is 5.

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