- Select a suitable instrument and quote readings with realistic precision.
- Measure length, volume and time, including very small lengths and short time intervals.
- Reduce random uncertainty by measuring multiples and calculating an average.
- Distinguish accuracy, precision, resolution, zero error and parallax error.
1.1 Choosing the correct measuring instrument
A measurement is a comparison with an agreed unit. The best instrument is not automatically the most sophisticated one; it is the instrument whose range and resolution match the size of the quantity. A metre rule is suitable for the length of a laboratory bench, whereas a micrometer is appropriate for the diameter of a thin wire. Using an instrument with unnecessarily coarse divisions limits the precision of the result.
Range is the largest value an instrument can measure. Resolution is the smallest change that can be detected directly. A millimetre ruler has a resolution of 1 mm, a typical analogue vernier calliper may resolve 0.1 mm, and a micrometer usually resolves 0.01 mm. The number of decimal places in the recorded result should reflect the instrument; writing many extra calculator digits does not make the original measurement more precise.
Before measuring, check for a zero error. If an instrument does not read zero when the true input is zero, every reading has a systematic offset. A positive zero error is subtracted from the observed reading; a negative zero error is added. In school practical work, the safest method is to record the zero reading explicitly and state the correction.
1.2 Measuring length correctly
Place the scale close to and parallel with the object. Read with the eye directly above the mark to avoid parallax. If the end of a ruler is damaged, start from another clear graduation and subtract the initial reading from the final reading. For the thickness of one sheet of paper or the diameter of a thin wire, measure a stack or several closely packed turns and divide by the number. This converts a very small distance into a larger, more reliable one.
An analogue micrometer has a sleeve (main scale) and a rotating thimble. First read the last visible whole or half millimetre on the sleeve. Then read the thimble division aligned with the datum line and multiply by 0.01 mm. Add the two contributions and then apply any zero correction. Use the ratchet gently so that the object is not compressed.
1.3 Measuring volume
A measuring cylinder should stand on a horizontal surface. Read the liquid level at eye height. For water and most common liquids, read the bottom of the concave meniscus. A narrow cylinder usually provides a finer scale and therefore a smaller reading uncertainty than a wide beaker.
The volume of a regularly shaped solid is calculated from its dimensions. For an irregular solid that sinks, note the initial volume V₁ of water, submerge the object completely without splashing or trapped air, and note the final volume V₂. The object volume is V₂ − V₁. If the object floats, use a sinker and perform an additional displacement reading so that the sinker contribution can be removed.
1.4 Measuring time and improving reliability
Human reaction time is often about a few tenths of a second, so it can be a large fraction of a short interval. Measure several repeated events in one timing. For a pendulum, time 10 or 20 complete oscillations and divide by the number to find the period. A complete oscillation means returning to the same position while moving in the same direction.
Repeat the whole measurement and calculate a mean. Repetition helps reveal anomalous results and reduces random variation, but it does not remove a systematic error such as a miscalibrated timer. A good record includes units in the table heading, consistent decimal places, and enough repeats to identify the spread.
1.5 Accuracy, precision and uncertainty language
Accuracy describes how close a result is to the true or accepted value. Precision describes how closely repeated readings agree and is linked to the spread and the instrument resolution. A set of readings can be precise but inaccurate if all are shifted by a zero error.
At O Level, uncertainty is often discussed qualitatively. A single analogue reading is commonly taken to have an uncertainty of about half the smallest division, while a difference calculated from two readings contains uncertainty from both endpoints. Percentage uncertainty is larger when the measured quantity is small, which is why measuring a stack of sheets is better than measuring one sheet directly.
Worked examples
The sleeve shows 5.5 mm and the 28th thimble division aligns with the datum line. The observed reading is 5.5 + 0.28 = 5.78 mm. If the micrometer has a +0.03 mm zero error, the corrected diameter is 5.78 − 0.03 = 5.75 mm.
Twenty oscillations take 31.6 s, 31.9 s and 31.7 s. Mean time = 31.73 s, so period T = 31.73/20 = 1.5865 s. Since the timer readings are to 0.1 s, a sensible reported period is 1.59 s.
Practical focus
Measure the diameter of a wire in at least three positions and at two perpendicular orientations. This tests whether the wire is uniform and circular. Record the zero reading, all observations and the mean corrected diameter.
Examination guidance
- State the instrument and explain why it is suitable.
- Do not write “human error” by itself. Name the actual issue, such as parallax, reaction time or difficulty judging the meniscus.
- A repeat is not automatically an improvement; explain how the mean or a larger measured interval reduces random uncertainty.
Check your understanding
- Why is timing 20 oscillations better than timing one?
- A ruler reads 1.3 cm at one end of a rod and 14.8 cm at the other. Find the length.
- What type of error is caused by consistently viewing a scale from an angle?
- The measured interval is much larger compared with the reaction-time uncertainty, so the percentage uncertainty is reduced.
- 14.8 − 1.3 = 13.5 cm.
- Parallax produces a systematic shift if the viewing position is consistently wrong.
