Key relationship
For nearest-division rounding on an ideal scale, the bound is ± least count / 2.
Physics · Class 11
Precision ruler
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.
Open the interactive experiment →How closely can your ruler see?
அளவுகோலின் மிகச் சிறிய பிரிவே மீச்சிற்றளவு. சிறிய பிரிவுகள் அளவீட்டின் நுணுக்கத்தை உயர்த்தும்; ஆனால் எல்லா பிழைகளையும் நீக்காது.
Key notes, relationships and model limits
Remember
Read from the correct zero and keep the line of sight perpendicular to the scale.
Common trap
More decimal places do not guarantee a more accurate measurement.
Model limits
The rounding bound excludes calibration, alignment and reading errors; finer resolution alone does not remove them.
What you will learn
Change scale division; compare readings; distinguish precision, accuracy and calibration error.
Try the experiment
Change the object length or the scale. Compare the rounded reading and its rounding-only bound.
Think of it this way
A bus timetable rounded to five minutes cannot tell you the exact second of arrival. A measurement also has a resolution.
Worked example
A 4.37 cm object reads 4.4 cm on a 0.1 cm ideal scale. Its rounding-only bound is ±0.05 cm.
Why this matters
A sharp scale still reads inaccurately if its zero is wrongly calibrated. Repeated readings do not necessarily remove this systematic bias.
Before you start
Decimals · fractions · powers of ten
Check your understanding
An ideal ruler has divisions 0.1 cm apart. What is the rounding-only bound?
- ± 0.1 cm
- ± 0.05 cm
- No uncertainty
Read the explanation
Nearest-division rounding has a maximum error of half a division: 0.1 / 2 = 0.05 cm. Real errors may add to this.
Course connection: CBSE XI Chapter 1; NEET/Main Unit 1; JEE Advanced General. Depth and exam wording differ.