It reduce measurement error due to resolution. For instance if your minimal resolution is 1 mm, your error due to that single measurement is +-0.5mm but if you increase the number of circunferentes in one measurement you will still have +-0.5mm of error due to resolution but you can divide the final measurement by N and get a lower error. Sorry if a didn't express myself but English is not my first language.

I hope the following table helps.

Be

1C + E = 10mm +- 1mm

2c + e = 20mm +- 1mm-> c = 10+-0.5mm

3c +e = 30mm +-1mm ->c = 10+-0.33mm

But C itself has error, so this table wouldn't work. I think your point is that the scale error remains the same and the percentage error decreases, but for the real measurement you can't just divide the error by the multiple of C.

Well it actually works for real world, but i may explained wrong. You wouldn't find the exact value of c since as you said the measurement comes with an error. but you will get a better approximation of c.

m1 = 10.1 so c = 10.1

m2 = 20.1 so c = 10.05

m3 = 30.1 so c = 10.03333

But the real value of c is 10.

Of course only applies if the measurement instrument is calibrated for the measured distance, and only works for resolution error.

my previous table is the same as said c must be between 9 and 11 ; 9.5 - 10.5 ; 9.6666 - 10.333.

-What it actually does is to reduce the significance of the error in the measurement.

This is different than mesurare one c, then start over and measure other c, then star over and measure other c, then add all three measurements together and then divide by three.

((c + e1)+(c + e2) +(c+e3))/3

Hope this was helpful.