To read an instrument, add the main scale reading to the fine scale reading, then correct for zero error. The uncertainty describes how precisely you can read the scale.
This lesson is part of SPM Physics measurement. Reading a value correctly also depends on the units from converting SI prefixes and units.
How do you read a micrometer?
Micrometer reading = sleeve reading + thimble reading × 0.01 mm.
Worked example. The sleeve shows 5.5 mm and the thimble line 23 is level with the datum line. The reading is 5.5 + 23 × 0.01 = 5.5 + 0.23 = 5.73 mm.
How do you read a vernier caliper?
Vernier reading = main scale reading + vernier division × 0.01 cm (each vernier division is 0.01 cm, so the caliper reads to 0.1 mm).
Worked example. The zero of the vernier scale is just past 2.3 cm on the main scale, and the 6th vernier mark lines up with a main scale mark. The reading is 2.3 + 6 × 0.01 = 2.36 cm.
How do you correct for zero error?
Close the jaws with nothing inside. If the scale does not read zero, that reading is the zero error, and it keeps its sign.
Corrected reading = observed reading − zero error.
Worked example A. Observed 5.73 mm, zero error +0.02 mm. Corrected = 5.73 − 0.02 = 5.71 mm.
Worked example B. Observed 6.41 mm, zero error −0.03 mm. Corrected = 6.41 − (−0.03) = 6.41 + 0.03 = 6.44 mm.
The mistake that costs marks
The common slip is to add the zero error whenever it appears in a question. Whether you add or subtract depends on its sign.
| Zero error | Wrong | Right |
|---|---|---|
| +0.02 mm (observed 5.73 mm) | 5.75 mm | 5.71 mm |
| −0.03 mm (observed 6.41 mm) | 6.38 mm | 6.44 mm |
Think of it this way: if the instrument reads too high with nothing inside, the true value is lower, so you subtract.
What uncertainty do you quote?
For an analogue scale, a common estimate is half the smallest division. A ruler marked in millimetres gives ±0.5 mm. A reading of 45 mm is then written as 45 ± 0.5 mm, unless your teacher uses another rule.
Check yourself
A micrometer shows a sleeve reading of 6.0 mm and a thimble reading of 41 divisions. Its zero error is −0.03 mm. Find the corrected reading.
Answer
Observed reading = 6.0 + 41 × 0.01 = 6.41 mm.
Corrected = 6.41 − (−0.03) = 6.44 mm.
A negative zero error means the instrument reads low, so the true value is larger than the observed reading.
What to study next
Next, use readings in graphs with plotting a graph with appropriate scale and units. For deeper data reasoning, see uncertainty and practical-data reasoning.
The units and significant-figure checker helps with presenting readings. If you want a teacher to check your readings, see online one-to-one Physics tuition.