Rounding errors and buying an "Extra Decimal"
Technically, nothing weighs 175 lb... if it does, it weighs 175.00000000000... to your heart's content

This article is not meant to be an authority on statistics, but simply an explanation of why we recommend buying an "extra decimal" whenever possible. Rounding errors are a seldom discussed, but ever-present factor in the scale industry, and something the consumer should be made more aware of.

All scales have a displayed resolution, whether 1 lb or 0.0001g. The displayed resolution is how "accurate" the scale is. It is essentially a compromise between reality and budget. Let me explain.

I will use human body weight as an example. Let's assume that I weigh 175 lbs... In reality, let's assume that technically speaking, I weigh 174.937678540283 lbs.

To illustrate how a scale (in general) would display how much I weigh, here is a list illustrating how scales decide between competing resolutions, all of which are "accurate" based on the scale's displayed resolution.

2 lb resolution: 174 lbs (closer to 174 than it is 176)
1 lb resolution: 175 (closer to 175 than 174)
0.1 lb resolution: 174.9 (closer to 174.9 than 174.8 or 175.0)
0.05 lb resolution: 174.95 (closer to .95 than .90)
0.02 lb resolution: 174.94 (closer to .94 than .92)
0.001 lb resolution:174.938 (closer to .938 than .937) *** This is the real illustration.

As you can see, (in general) a scale will display a value based on the REAL weight always being something other (more specific) than a resolution...

SO, if your application is something that requires the resolution of 0.001g (for example) in any situation, a perfectly calibrated balance will still display at worst a rounding error of 0.0004g - if in reality the sample weighs 112.3456g - the balance will display the resolution 0f 112.346g- a difference of 0.0004g

This 0.0004g does not appear on the scale, and will likely only influence your results when doing formula work, compounding, etc.

If your application requires accuracy to a certain spec, and budget allows, we recommend buying an extra decimal place.... in practice, this will allow you to know when you are at the desired volume of additives - without worrying about rounding errors in the single digit %.

Austin H.
General Manager

Author: Summit Measurement