PRECISION / THE SMALLEST STEP
How closely can your ruler see?
A ruler can only distinguish its marked divisions. Its least count is the smallest interval it can read. A finer scale reduces rounding uncertainty, but does not automatically remove calibration or reading errors.
அளவுகோலின் மிகச் சிறிய பிரிவே மீச்சிற்றளவு. சிறிய பிரிவுகள் அளவீட்டின் நுணுக்கத்தை உயர்த்தும்; ஆனால் எல்லா பிழைகளையும் நீக்காது.
A bus timetable rounded to five minutes cannot tell you the exact second of arrival. A measurement also has a resolution.
Observe: change the scale division, compare readings, and explain why precision differs from accuracy.
Change the object length or the scale. Watch the rounded reading and its resolution bound change.
Model: ideal calibrated ruler, object starts at zero, rounding to the nearest division. The ± half-division bound covers rounding only; it is not a measured standard deviation or total experimental uncertainty.
Model: SI mechanical dimensions L, M, T. A mismatch disproves a proposed relation. A match is necessary but does not establish correctness or determine dimensionless constants.
Pause. Predict. Explain.
An ideal ruler has divisions 0.1 cm apart. What is the rounding-only uncertainty bound?
The largest rounding error is half the distance between adjacent divisions: 0.1 / 2 = 0.05 cm. Other real experimental errors may add to this.