Significant Figures & Units

Practical Skills - OCR A-Level Physics

Key Definition

Significant Figures
The digits in a number that carry meaningful information about its precision. They indicate which digits are reliable and necessary to express the quantity.

Rules for Identifying Significant Figures

All non-zero digits are significant (e.g. 473 has 3 s.f.).
Zeros between non-zero digits are significant (e.g. 4107 has 4 s.f.).
Leading zeros are not significant -- they only position the decimal point (e.g. 0.00079 has 2 s.f.).
Trailing zeros in whole numbers (without a decimal point) are not significant (e.g. 57,000 has 2 s.f.).
Trailing zeros after a decimal point are significant (e.g. 45.00 has 4 s.f.).

Rounding to Significant Figures

Step 1: Identify the significant figures using the rules above.
Step 2: Count to the required number from the first significant figure.
Step 3: Look at the next digit (the "decider"). If it is 5 or greater, round up; if less than 5, round down.
Example: 1.0478 to 3 s.f. The third significant figure is 4, the decider is 7 (round up), so the answer is 1.05.

Standard Form

Key Definition

Standard Form
A way of expressing very large or very small numbers as $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer. For example, $1.6 \times 10^{-19}$ C.

SI Prefixes

Common prefixes: T (tera, $10^{12}$), G (giga, $10^{9}$), M (mega, $10^{6}$), k (kilo, $10^{3}$), c (centi, $10^{-2}$), m (milli, $10^{-3}$), μ (micro, $10^{-6}$), n (nano, $10^{-9}$), p (pico, $10^{-12}$).
Always convert to SI base units before performing calculations.

Practical Application

Match the number of significant figures in your answer to the least precise measurement used in the calculation.
Example: multiplying 4.5 (2 s.f.) by 12.789 (5 s.f.) should be reported to 2 s.f.: 58, not 57.5505.
All data in a table column should be quoted to the same number of significant figures or decimal places.
When calculating mean values, it is acceptable to increase the number of significant figures by one.

Recording Measurements

Digital instruments: record all digits shown on the display. Exception: for stopwatches, no need to record more than 2 d.p.
Analogue instruments: record all figures known with certainty, plus an additional estimated figure where appropriate.
Always include the correct unit with every measurement.
In tables, label columns as Quantity / Unit (e.g. "Length / m"), using a forward slash.

Common MistakeMEDIUM

Wrong: Giving a final answer to more significant figures than the least precise measurement used (e.g. quoting 57.5505 when one input was only 2 s.f.).
Right: Round the final answer to match the least precise input. Overstating precision can lose marks in exams.

N = A \times 10^n, \quad 1 \le A < 10

Diagram pending

Vertical ladder of SI prefixes from tera ($10^{12}$) down to femto ($10^{-15}$), with each row showing symbol, multiplier in standard form, and a worked example (e.g. $5 \text{ mA} = 5 \times 10^{-3} \text{ A}$).

Will be replaced with a GeoGebra SVG in stream 2.

Examiner Tips and Tricks

Convert every prefixed value to SI base units before substituting into a formula. A 5 mF capacitor is $5 \times 10^{-3} \text{ F}$; forgetting the milli is the most common slip in capacitor calculations.
Axis titles always read "Quantity / unit" (e.g. $v / \text{m s}^{-1}$). The forward slash is the standard divider, with any power of ten placed after the slash and before the unit.
Stopwatch readings should be quoted to 2 d.p. ($0.01 \text{ s}$) even though human reaction time is much larger, because that is the instrument resolution.