7. Rounding Methods
Rounding becomes an issue when the next digit after the last to be kept is a 5. Computers and most people round up if the following digit is a 5 (this is the 4/5 rounding rule: 4 or less, leave alone; 5 or more, round up).
Example: 34.65 to 3 sig fig rounds to 34.7
This approach works well for most cases.
Surveyors, on the other hand, use an even rounding rule when the next digit is a 5;
- if the last digit to be kept is even, it is left as is,
- if the last digit to be kept is odd, it is increased to the next even.
34.65 to 3 sig fig rounds to 34.6
18.215 to 4 sig fig rounds to 18.22
If you follow the surveyor’s rule, what about numbers which follow the 5?
For example how would you round 12.5496 to 2 sig fig?
Is .5496 greater than .5 so in this case we’d round to 13?
Remember what sig fig are: the digits of which we’re certain plus an estimate. The 5 isn’t a sig fig - the preceding digit is and that’s an estimate. We’re using the 5 to refine that estimate. The 5 is 10 times less significant than the estimate, the following 4 is 100 times less significant, and so on. Basically, anything after the 5 is garbage, noise, and can be ignored: key only on the 5.
Therefore, 12.5496 to 2 sig fig would round to 12.
So why do surveyors use this rule? Well, for many non-digital measuring devices, the smallest division can usually be estimated to 1/2. That means there’s a 50/50 chance of estimating incorrectly. If we always rounded up when encountering a 5 (the half-division), then the rounding would always be biased in one direction. By using the even rounding rule, sometimes we round up, sometimes down; in the end it evens out (we’re really quite a clever bunch).
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