3.2.3Development of Practical Skills in Physics
Significant Figures
5 min read 9 parts Lesson 28 of 29 1 quiz
Lesson summary
3.2.3 Significant Figures — EDEXCEL IAL PHYSICS (IAS & A2) notes: Count significant figures, round correctly and record data and results to an appropriate precision.Significant figures = the digits in a number that are reliable and necessary to indicate the quantity.Use — signifi…
- Exam marks
- Intermediate steps
- Resolution
- Trailing zeros
- Micrometer
- Multiplying or dividing
Section 1 of 9What significant figures are
Significant figures
Significant figures the digits in a number that are reliable and necessary to indicate the quantity.
Use
- Use significant figures must be used when dealing with quantitative data.
Exam marks
- Exam marks a question may state the number of significant figures required, and a mark is often given for it.
Section 2 of 9Rules for counting
| Rule | Examples |
|---|---|
| All non-zero digits are significant | 4107 has 4 s.f. |
| Zeros between non-zero digits are significant | 29.009 has 5 s.f. |
| Zeros before all non-zero digits are not significant | 0.00079 has 2 s.f.; 0.48 has 2 s.f. |
| Trailing zeros in a number without a decimal point are not significant | 57,000 has 2 s.f.; 640 has 2 s.f. |
| Zeros after non-zero digits within a number with decimals are significant | 689.0023 has 7 s.f. |
Section 3 of 9Rounding
1
Identify the significant figures using the rules.
2
Count from the first significant figure to the required number.
3
Look at the next digit (the decider).
4
If the decider is 5 or greater, increase the last kept digit by 1.
- Intermediate steps
- do not round intermediate values until the final answer.
Section 4 of 9Raw data
Resolution
- Resolution record each reading to the resolution of the instrument, with a consistent number of decimal places.
Trailing zeros
- Trailing zeros keep them if the display shows them.
- (2.40 V, not 2.4 V)
Micrometer
- Micrometer readings are quoted to 3 significant figures, e.g. 2.30 mm.
Typical
- 3 significant figures is usual for data that will be plotted.
Section 5 of 9Calculated results
Multiplying or dividing
- Multiplying or dividing no more significant figures than the least precise input.
Adding or subtracting
- Adding or subtracting the same number of decimal places as the least precise input.
Column consistency
- Column consistency all values in a column have the same number of significant figures.
Means
- Means it is acceptable to give a mean to one more significant figure than the readings.
Section 6 of 9Uncertainties and final answers
Uncertainty
- Uncertainty quote to one significant figure, then match the value to the same decimal place.
- (two if it starts with 1)
Gradients
- Gradients two or three significant figures are usually appropriate.
Standard form
- Standard form writing 2.50 × 102 m makes the number of significant figures clear.
Section 7 of 9More from the specification
1Precision limits on instrument scale
- Precision limits on instrument scale recording experimental quantities to consistent significant figures reflects the smallest graduation interval on the measuring scale.
2Significant Figures Convention
- In experimental physics, calculated quantities should be quoted to the same number of significant figures as the raw measurement with the least precision.
3Timing Oscillations with Fiducial Markers
- In a mass-spring or pendulum experiment, timing 10 or 20 complete oscillations past a central fiducial marker minimizes human reaction time error in the measured period.
4Identifying and Discarding Anomalies
- Repeated measurements taken over an experimental range must be inspected for anomalous values before calculating a representative mean.
5Appropriate Choice of Measuring Instruments
- Measuring length or extension using a metre ruler provides millimetre resolution (± 1 mm),
- whereas a micrometer screw gauge is needed for wire diameter (± 0.01 mm).
6Significant Figures Convention
- In experimental physics, calculated quantities should be quoted to the same number of significant figures as the raw measurement with the least precision.
7Timing Oscillations with Fiducial Markers
- In a mass-spring or pendulum experiment, timing 10 or 20 complete oscillations past a central fiducial marker minimizes human reaction time error in the measured period.
8Identifying and Discarding Anomalies
- Repeated measurements taken over an experimental range must be inspected for anomalous values before calculating a representative mean.
9Appropriate Choice of Measuring Instruments
- Measuring length or extension using a metre ruler provides millimetre resolution (± 1 mm),
- whereas a micrometer screw gauge is needed for wire diameter (± 0.01 mm).
10Fiducial marker alignment
- Fiducial marker alignment placing a fiducial marker at equilibrium marks the period of oscillations accurately when measuring elapsed time.
11Experimental range and intervals
- Experimental range and intervals planning measurements across an extended range with uniform intervals reveals genuine trends in experimental results.
12Timing multiple periods
- Timing multiple periods timing ten oscillations on a stopwatch minimizes timing errors before calculating the single period.
13Apparatus
- The equipment needed to carry out an experiment.
14Extension
- Increase in length over the original length.
15Anomalous reading
- A measurement that does not fit the pattern of the other data.
16Fiducial marker
- A fixed reference mark used to judge when an oscillating object passes its centre position.
17Potential difference
- Work done by a unit charge passing through a component.
18Elastic limit
- Greatest load a spring can recover from.
19Anomalous result
- A result that does not fit the trend of the other data.
20Oscillation
- Repeated back-and-forth motion.
21Period
- Time for one revolution.
22Error
- The difference between a measurement and the true value.
23Current
- Flow of electrons in a circuit.
24Pendulum
- A weight swinging on a string, exchanging GPE and KE.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Significant figure | A digit that contributes to the precision of a number. |
| Decimal place | A digit to the right of the decimal point. |
| Standard form | A number written as a × 10n. |
| Rounding | Reducing the number of digits and adjusting the last one kept. |
| Precision | Closeness of repeated measurements, shown by the figures recorded. |
Section 9 of 9Exam technique
1
Writing a calculator display such as 12.32142857 as the answer.
2
Dropping trailing zeros from a reading — write 2.40 when the display shows 2.40.
3
Giving an uncertainty to more places than the value, or the value to more places than the uncertainty allows.
4
Rounding in the middle of a multi-step calculation.