| Random errors affect precision by causing differences in measurements, leading to a spread about the mean. | Random Errors |
| What do random errors affect in measurements? | Precision. |
| Electronic noise in the circuit of an electrical instrument is an example of a random error. | Example of Random Error |
| Can all random errors be eliminated? | No, you cannot get rid of all random errors. |
| Take at least 3 repeats and calculate a mean to reduce random errors and identify anomalies. | Reducing Random Errors - Repeats |
| How can taking multiple repeats help with random errors? | It reduces errors and helps identify anomalies. |
| Use computers, data loggers, or cameras to reduce human error and enable smaller intervals in measurements. | Reducing Random Errors - Technology |
| How can computers or data loggers help in reducing random errors? | They reduce human error and allow smaller intervals between measurements. |
| Use equipment with higher resolution, e.g., a micrometer (0.1 mm) instead of a ruler (1 mm) for more precise measurements. | Appropriate Equipment |
| Why is using a micrometer better than a ruler for reducing random errors? | A micrometer has higher resolution (0.1 mm) than a ruler (1 mm), leading to more precise measurements. |
| Systematic errors affect accuracy and are caused by the apparatus or faults in the experimental method. They make all results too high or too low by the same amount. | Systematic Errors |
| What do systematic errors affect? | Accuracy. |
| A balance that isn’t zeroed correctly (zero error) or reading a scale at a different angle (parallax error) are examples of systematic errors. | Example of Systematic Error |
| What is a zero error? | A type of systematic error where the balance isn’t zeroed correctly, causing inaccurate measurements. |
| Calibrate apparatus by measuring a known value, such as weighing 1 kg on a balance, to identify systematic errors. | Reducing Systematic Error - Calibration |
| How can calibrating apparatus help reduce systematic errors? | It helps identify inaccuracies by comparing the measured value to a known reference. |
| In radiation experiments, correct for background radiation by measuring it beforehand and excluding it from final results. | Reducing Systematic Error - Radiation Experiments |
| How can background radiation be corrected in radiation experiments? | Measure it beforehand and exclude it from the final results. |
| To reduce parallax error, read the meniscus at eye level when measuring liquids. | Reducing Parallax Error |
| What is the best way to read the meniscus to reduce parallax error? | Read it at eye level. |
| Precise measurements are consistent and fluctuate slightly about a mean value. Precision doesn’t indicate that the value is accurate. | Precision |
| What does it mean for a measurement to be precise? | It means the measurements are consistent and fluctuate slightly around a mean, but this doesn’t necessarily mean the value is accurate. |
| If the original experimenter can redo the experiment using the same equipment and method and get the same results, the experiment is repeatable. | Repeatability |
| What is repeatability in an experiment? | It's when the same experimenter can repeat the experiment with the same equipment and method, getting the same results. |
| If an experiment is redone by a different person or with different techniques and equipment, and the same results are found, the experiment is reproducible. | Reproducibility |
| How is reproducibility different from repeatability? | Reproducibility refers to getting the same results when the experiment is redone by someone else or with different equipment or techniques. |
| Resolution is the smallest change in the quantity being measured that gives a recognisable change in reading. | Resolution |
| What does resolution measure in an instrument? | The smallest detectable change in the quantity being measured that causes a noticeable change in reading. |
| A measurement that is close to the true value is considered accurate. | Accuracy |
| What does accuracy mean in measurements? | A measurement is accurate if it is close to the true value. |
| The bounds within which the accurate value is expected to lie, e.g., 20°C ± 2°C, meaning the true value could be between 18°C and 22°C. | Uncertainty of a measurement |
| What does "20°C ± 2°C" signify? | The true value could be within 18-22°C, indicating the uncertainty range. |
| Uncertainty given as a fixed quantity, e.g., 7 ± 0.6 V. | Absolute Uncertainty |
| What is an example of absolute uncertainty? | 7 ± 0.6 V. |
| Fractional Uncertainty is given as a fraction of the measurement, for example, 7 V ± 3/35. | Fractional Uncertainty |
| How is Fractional Uncertainty expressed? | As a fraction of the measurement, for example, 7 V ± 3/35. |
| Percentage Uncertainty is given as a percentage of the measurement, for example, 7 ± 8.6% V. | Percentage Uncertainty |
| How is Percentage Uncertainty expressed? | As a percentage of the measurement, for example, 7 ± 8.6% V. |
| To reduce percentage and fractional uncertainty, measure larger quantities. | Reducing Percentage and Fractional Uncertainty |
| How can you reduce Percentage and Fractional Uncertainty? | By measuring larger quantities. |
| Readings are when one value is found, for example, reading a thermometer. | Readings |
| What is an example of a reading? | Reading a thermometer. |
| Measurements involve finding the difference between two readings, such as using a ruler (judging both the starting point and end point). | Measurements |
| How does a measurement differ from a reading? | A measurement finds the difference between two readings. |
| The uncertainty in a reading is ± half the smallest division, for example, with a thermometer where the smallest division is 1°C, the uncertainty is ± 0.5°C. | Uncertainty in a Reading |
| What is the uncertainty in a thermometer reading with a smallest division of 1°C? | ± 0.5°C. |
| The uncertainty in a measurement is at least ±1 smallest division, for example, with a ruler where each end has ± 0.5 mm, the total uncertainty is ± 1 mm. | Uncertainty in a Measurement |
| What is the uncertainty in a measurement using a ruler, where each end has ± 0.5 mm? | ± 1 mm. |
| For digital readings, the uncertainty is either quoted or assumed to be ± the last significant digit, for example, 3.2 ± 0.1 V. | Digital Readings |
| What is the uncertainty in a digital reading of 3.2 V? | ± 0.1 V. |
| For repeated data, uncertainty is half the range (largest - smallest value) and is shown as mean ± ½ range. | Uncertainty in Repeated Data |
| How is uncertainty in repeated data calculated? | Half the range and shown as mean ± ½ range. |
| You can reduce uncertainty by fixing one end of the ruler, so only the uncertainty in one reading is included. Another way is by measuring multiple instances. | Reducing Uncertainty in Measurements |
| How can you reduce uncertainty when using a ruler? | By fixing one end of the ruler or measuring multiple instances. |
| When measuring multiple instances, the uncertainty is divided by the number of instances, for example, measuring 10 pendulum swings and dividing the uncertainty by 10. | Uncertainty in Multiple Measurements |
| If measuring 10 swings of a pendulum, how is the uncertainty for 1 swing calculated? | Divide the total uncertainty by 10. |
| Uncertainties should be given to the same number of significant figures as the data. | Significant Figures in Uncertainty |
| To how many significant figures should uncertainty be given? | To the same number as the data. |
| When adding or subtracting data with uncertainties, add the absolute uncertainties. | Adding/Subtracting Data |
| A thermometer with an uncertainty of ±0.5 K shows a temperature drop from 298 ± 0.5 K to 273 ± 0.5 K. What is the difference in temperature? | Difference in temperature = 298 - 273 = 25 K
Add absolute uncertainties: 0.5 K + 0.5 K = 1 K
Final difference = 25 ± 1 K |
| When multiplying or dividing data with uncertainties, add the percentage uncertainties. | Multiplying/Dividing Data |
| A force of 91 ± 3 N is applied to a mass of 7 ± 0.2 kg. What is the acceleration of the mass? | a = F/m = 91/7 = 13 m/s²
Percentage uncertainty for force = (3/91) × 100 = 3.3%
Percentage uncertainty for mass = (0.2/7) × 100 = 2.9%
Total % uncertainty = 3.3% + 2.9% = 6.2%
6.2% of 13 m/s² = 0.8 m/s²
Final acceleration = 13 ± 0.8 m/s² |
| When raising a value to a power, multiply the percentage uncertainty by the power. | Raising to a Power |
| The radius of a circle is 5 ± 0.3 cm. What is the percentage uncertainty in the area of the circle? | Area = πr² = π × 5² = 78.5 cm²
Percentage uncertainty in radius = (0.3/5) × 100 = 6%
Percentage uncertainty in area = 6% × 2 (since r²) = 12%
Final uncertainty in area = 78.5 ± 12% cm² |
| Error bars on graphs represent uncertainties. For example, if the uncertainty is ±5 mm, the error bars extend 5 squares on either side of the data point. | Error Bars |
| How should a line of best fit be positioned relative to error bars on a graph? | The line of best fit should go through all error bars, excluding anomalous points. |
| To find the uncertainty in a gradient, draw the steepest and shallowest lines of worst fit through all error bars. The uncertainty is the difference between the best and worst gradient. | Uncertainty in Gradient |
| How do you calculate the percentage uncertainty in the gradient of a line? | Uncertainty = (|best gradient − worst gradient| / best gradient) × 100% |
| When the best and worst lines have different y-intercepts, the uncertainty in the y-intercept is calculated as |best y-intercept − worst y-intercept|. | Uncertainty in Y-Intercept |
| How do you calculate the percentage uncertainty in the y-intercept? | Uncertainty = (|best y-intercept − worst y-intercept| / best y-intercept) × 100% |
| Alternatively, the average of the two maximum and minimum lines can be used to calculate the percentage uncertainty. Percentage uncertainty = (max gradient − min gradient) / 2 × 100% | Alternative Calculation for Uncertainty |
