Measurement and Uncertainty for Integrated Programme (IP) Physics — From Sig-Figs to Spreadsheet Graphs

TL;DR — New syllabus = new marks.
Quote instruments to the correct significant figures, report uncertainties as \(\pm \frac{1}{2}\) least-division, and round calculated quantities to the smallest-sf raw datum.
Master absolute → fractional → percentage error conversions; propagate by addition for x / ÷, by sum of percentages for powers.
Paper 4 (practical) now explicitly allows — and tests — spreadsheet skills: gradients, intercepts, "=STDEV.S( )" and trend-lines.
Try the 20-s pendulum timing lab below; analyse your data with Sheets/Excel and you will have practised every assessed skill in one evening.

1 Why measurement & uncertainty just became high-stakes

Both O-level 6091 and A-level H2 (9478) syllabuses for 2026 list "handling experimental data, including spreadsheet processing" as an Assessment Objective worth up to 20 % of practical marks.

Specimen Paper 4 even states, "You may use a spreadsheet to process and analyse data.".

Private-tuition blogs warn that manual graph paper will be phased out, replaced by CSV uploads and Excel trend-lines.

2 Reading instruments & recording to the right sig-figs

2.1 Analogue versus digital

SEAB stipulates that "a measurement or calculated quantity must be accompanied by a correct unit, and calculated quantities should be given to the same number of significant figures as the least-sf raw datum."

For example, calculating \(R = V/I\) from 3 s.f. voltage and 2 s.f. current means your final \(R\) must be 2 s.f.

2.2 Sig-fig decision tree

1. Quote what the instrument shows — no truncation.
2. Intermediate steps: keep 1 extra sig-fig to suppress rounding drift.
3. Final line: match the least sig-fig among the raw inputs.

Worked example
\(I = 0.43 \space \pu{A}\) (2 s.f.), \(V = 3.05 \space \pu{V}\) (3 s.f.)
\(R = 7.09 \space \pu{Ω}\) (calculator) \(→\) round to 2 s.f. \(→ 7.1 \space Ω\).

3 Absolute, fractional & percentage uncertainty

Rule-of-thumb: when you add/subtract, add absolute uncertainties; when you multiply/divide or raise to a power \(n\), add percentage uncertainties and multiply by \(n\).

Quick drill

A meter measures \(L = 0.381 \pm 0.002 \space \pu{m}\).
Percentage uncertainty \(= \frac{0.002}{0.381}\times100 = 0.52\%.\)

Community examples show the same propagation applied to pendulum \(g\) calculations.

4 Spreadsheet skills now examinable

SEAB's 2026 guide specifies that candidates must be able to **"process and analyse data using spreadsheet software, including calculating gradient and area under curves." Practically, that means you should know how to:

1. Import a .csv file or type raw readings.
2. Use =AVERAGE(range) and =STDEV.S(range) for mean & sd.
3. Plot an XY Scatter, add a linear trend-line, tick Display equation and R².
4. Extract gradient/intercept directly from the equation box (e.g. \(y = 3.21x + 0.05\)).
5. Calculate % uncertainty of gradient with the built-in LINEST() function (advanced but examinable).

5 Mini-Lab: Timing a pendulum with your phone & Sheets

This 30-minute activity rehearses every skill the syllabus demands.

5.1 Setup

• String, small metal nut, metre rule, phone timer/camera.
• Measure \(L\) three times; take the mean length. Record to the nearest millimetre.

5.2 Data collection

1. Displace < 15° (small-angle).
2. Start timing on the first crossing; record 20 oscillations to reduce percentage timing error.
3. Repeat x 5 trials.

Reaction time of 0.2 s roughly halves when timing 20 periods versus one, cutting % uncertainty dramatically.

5.3 Spreadsheet crunch

1. In Sheets, enter \(L\) and corresponding \(T\).
2. Create columns for \(T^{2}\) and \(\ln T\) if you wish to test alternative models.
3. Plot \(T^{2}\) vs \(L\); gradient \(m = \frac{4\pi^{2}}{g}\).
4. Use =LINEST(T2_range, L_range, TRUE, TRUE) to obtain \(m\) and its standard error; convert to % uncertainty.

Sample output: \( \lbrace 4.045, 0.013 \rbrace \) → gradient \(4.05 \pm 0.01\). Hence \(g = \frac{4\pi^{2}}{4.05} = 9.74 \space \pu{m.s-2}\) with \(\pm\space 0.02 \space \pu{m.s-2}\) absolute uncertainty \(0.2 \%\).

Compare to the accepted \(9.81 \space \pu{m.s-2}\); percentage error = 0.7 %, comfortably within combined uncertainties.

6 Nine examiner-liked habits to lock in marks

1. Underline units every time you write a number.
2. Quote \(\pm\) uncertainty beside every raw reading in a table.
3. Choose axis scales that use > 50 % of the graph grid; spreadsheets do this automatically but check tick step.
4. Use 3 s.f. for gradients/intercepts if raw data are 3 s.f.
5. Mark anomalous points with a small x and omit from trend-line only with justification.
6. State limiting factor ("reaction time dominates timing error") in ACE write-ups.
7. Check \(R^2 > 0.995\) for a good fit; if not, discuss curvature.
8. Propagate uncertainty before simplifying results (avoid rounding too early).
9. Round final answers at the last line only.

7 Quick self-check

1. A digital balance reads 85.32 g. Quote the absolute uncertainty.
2. Combine \(V = 5.01 \pm 0.05 \pu{V}\) and \(I = 0.20 \pm 0.01 \pu{A}\); state \(R\) with % uncertainty.
3. Why does doubling the number of pendulum oscillations timed reduce % error?
4. Describe two spreadsheet commands that replace manual graph tasks.
5. Your LINEST() output gives gradient \(3.98 \pm 0.15\). What is the percentage uncertainty in \(g\)?

(Answers in collapsible spoiler at the bottom of the page.)

8 Further reading

• [PDF] SEAB — H2 9478 Physics Syllabus (2026).
• [PDF] SEAB — O-Level 6091 Physics Syllabus (2026) for sig-fig policy.
• IOP Spark — Investigating the time of oscillation of a pendulum.
• LibreTexts sample lab — Measuring \(g\) with a pendulum.
• SaveMyExams — A-level significant-figures rules.
• SmartLab blog — spreadsheet requirement commentary.

Next step: plug your pendulum data into a spreadsheet tonight, post a screenshot in class chat, and tag a friend to audit your uncertainty table.