Quick Summary

1. Number of Readings

Here's the thing about a single measurement: it could be wrong, and you'd never know. Maybe your reaction time was off, maybe there was a random gust of wind, maybe you misread the scale by a hair. A single reading has no way of checking itself.

That's why we take repeat readings — usually 3 to 5 times for the same value of the independent variable. Then we average them. Averaging repeats does three jobs at once:

• Increases precision — random errors tend to cancel out when you average, so your value clusters closer to the "true" one.
• Increases confidence — if your three readings are all close together, you know it wasn't a fluke.
• Checks reproducibility — if repeats scatter wildly, that tells you something is unstable in your method, and you'd want to investigate before trusting the data.

Recording to the right precision

Every instrument has a resolution — the smallest change it can actually detect. Your recorded values must match that resolution consistently. For example:

• A micrometer (resolution 0.01 mm) → record to 2 decimal places, e.g. 1.40 mm, not 1.4 mm.
• A ruler measuring in cm (resolution 0.1 cm) → record to 1 decimal place, e.g. 5.3 cm.
• A ruler measuring in metres (resolution 0.01 m / 1 mm) → record to 2 decimal places, e.g. 0.35 m.

Beyond raw resolution, final calculated answers are usually quoted to 3 significant figures — this is generally the level of precision you can confidently read off a graph or trust in a calculation.

2. Range of Measurements

Taking repeats tells you how reliable a single point is. But you also need enough different points across a wide enough range to see the full shape of the relationship you're investigating. Aim for 5 to 10 values, evenly spaced with a step of 1, 2, 5, or a multiple of 10 (never something awkward like steps of 0.3, 0.6, 0.9).

Why range matters — the diode example

Imagine plotting current against potential difference (V) for a semiconductor diode. If you only measured up to 0.5 V, your graph would look like a flat horizontal line — completely uninteresting, and you'd conclude "current doesn't really change with voltage." But diodes have a threshold voltage where current suddenly shoots up. If you extend your range up to 3 V, you'd suddenly see a steep, almost vertical rise in current. A narrow range can completely hide the real physics.

What limits your range?

You can't always just pick any range you like — think about two things:

• The instrument's own range — a 1 m ruler shouldn't be asked to measure up to 5 m; you'd run out of ruler and introduce big errors trying to "extend" the measurement.
• The apparatus's physical limits — e.g. don't stretch a spring past its elastic limit, and don't push voltage/current so high that a component overheats or burns out.

3. Significant Figures

Significant figures (s.f.) are the digits in a number that actually carry meaningful information about its size — not just placeholders. Getting this right matters because it tells anyone reading your data exactly how precisely you measured something.

The Rules

How to round to a given number of s.f.

1. Identify all the significant figures using the rules above.
2. Count from the first significant figure up to the number you need.
3. Look at the next digit — this is the "rounder decider."
4. If that decider digit is 5 or more, round the previous digit up by 1. If it's less than 5, leave it alone.

4. Anomalous Readings

Sometimes, no matter how careful you are, one reading in a set just doesn't fit. Maybe you misread the scale, maybe the stopwatch wasn't started in time, maybe there was a one-off disturbance. These are called experimental errors (also known as operator errors, or "one-off" errors), and they produce what we call anomalous results — or anomalies for short.

How do you spot one?

An anomaly is a result that is inconsistent with the rest of your data — either it doesn't fit the trend on a graph (it sits well off the line of best fit), or it's wildly different from your other repeat readings for the same value.

What do you actually DO about it?

Two steps, always in this order:

• Ignore the anomalous value when calculating your mean — don't let one bad reading drag your average off course.
• Repeat that particular measurement, if you have time, to get a proper replacement reading.

Removing anomalies makes your data more precise, which in turn lets you draw more valid conclusions at the end of the experiment.

5. Using a Micrometer

A micrometer (or micrometer screw gauge) is used for measuring very small widths, thicknesses, or diameters — like the diameter of a copper wire. It's far more precise than a ruler, with a resolution of 0.01 mm.

The parts you need to know

• Main scale — sits on the sleeve/barrel, fixed in place.
• Thimble scale — the rotating scale, each division = 0.01 mm.
• Anvil & spindle — the two surfaces that clamp around your object.
• Ratchet — the correct way to tighten the spindle onto the object.

How to take a reading

1. Read the main scale first — each division = 0.5 mm. Read to the nearest 0.5 mm mark visible before the thimble edge.
2. Read the thimble scale — find which line on the thimble aligns with the central horizontal line of the main scale. Each division = 0.01 mm.
3. Multiply the thimble reading by 0.01 mm.
4. Add the main scale reading and thimble reading together.

6. Evaluating Experiments

Once you've done the experiment, the examiner wants to see that you can think critically about it — where might errors creep in, and how could the method be improved? Two big levers here: repeating measurements (boosts accuracy via averaging) and reducing systematic errors (shifts your whole data set closer to the true value).

Case Study: Timing Oscillations

A classic exam scenario is timing a pendulum with a stopwatch. The problem? Human reaction time introduces a small but real error every single time you start/stop the watch. If the time period of one oscillation is short, that fixed reaction-time error becomes a huge fraction of your measurement.

Fiducial Markers

A fiducial marker is simply a fixed reference point (e.g. a pin with blu-tack, positioned exactly at the pendulum's centre of oscillation) that helps you time consistently. You sight the pendulum bob as it crosses this marker.

Crucially, you should time the pendulum as it passes the marker at its lowest point — because that's where it's moving fastest. A fast-moving object is easier to time precisely because it "snaps" past the marker in an instant, whereas at the top of the swing it lingers, making the exact moment of passing harder to judge.

Set Squares & Plumb Lines

In mechanics experiments, small alignment errors can quietly wreck your data. A set square (a right-angled triangle) checks whether two things are perpendicular, parallel, or vertical. A plumb line (a weight hanging from a string) shows true vertical using gravity.

Classic use case: checking a ruler is truly vertical alongside a stretching spring. If the ruler leans even slightly, your "extension" reading will be a foreshortened, inaccurate version of the real extension — and since extensions are often small already, this error can be proportionally huge.

What to Memorise

Concepts Checklist

Exam Tips & Common Mistakes