Some of the trickier aspects of accuracy are explained here. Using some of these techniques will allow you to present your data in the best possible way. By presenting your results in a precise manner you indicate that you are aware of the importance of considering the accuracy of your results. This is often one of the deciding factors between awarding 6 or 8 marks. You also need to bear in mind that to carry out a detailed mathematical analysis into the reliability of your results would be well beyond the scope of GCSE Science. You should, however, have some feeling for the processes involved and be able to identify the factors that limit the accuracy of your experiment.
If you look at the example table below you will see that all the results are written to a consistent number of figures. Note 40.0 cm rather than 40 cm. The distances are all measured to the nearest mm, the speeds to the nearest 0.1 m/s.
| distance (cm) |
speed (m/s) | average speed (m/s) |
||
|---|---|---|---|---|
| 1st | 2nd | 3rd | ||
| extract from results | ||||
| 20.3 | 0.6 | 0.7 | 0.7 | 0.67 |
| 29.7 | 0.5 | 0.4 | 0.6 | 0.50 |
| 40.0 | 0.3 | 0.3 | 0.4 | 0.33 |
| 50.2 | 0.2 | 0.3 | 0.2 | 0.23 |
| 59.8 | 0.3 | 0.2 | 0.1 | 0.20 |
The average speed is written to an extra decimal place because most of the speed values only have one significant figure. This prevents a loss in accuracy and may result in a smoother graph when the points are plotted. If the raw speed values had more significant figures (e.g. 1.31 m/s) this would not be so important.
Suppose we are using a digital ammeter to measure current. The ammeter has two scales, 0 to 10 Amps, and 0 to 200 mA.
The first reading is taken on the 10 A scale and reads 0.25 A. The second reading is 0.19 A on the same scale. This value is now less than 200 mA so we can switch down a scale; we would switch scale to get (hopefully) better accuracy. On the 200 mA scale the second reading is now 193 mA; this gains an extra digit of precision.
When putting these results into a table we either want all the results in amps or milliamps - we don't want both. In doing this we want to preserve the actual value given on the display of the ammeter and not change the precision. To convert these properly you must take careful note of the number of significant figures. The amp measurement has 2 (zeros before the first number don't count), the milliamp measurement 3 significant figures.
| current (A) |
Both in amps: Note that the correct number of significant figures must be preserved. 0.250 A would, technically, be incorrect and would show an extra place of precision that was not available on the ammeter. |
|---|---|
| 0.25 | |
| 0.193 | |
| current (mA) |
Both in milliamps: Note that to show the correct number of figures you have to use standard form. Again, 250 mA would show an extra place of precision that does not exist. |
| 2.5×102 | |
| 1.93×102 | |
| 193 | |
Putting your answers in Amps is probably best, however it all depends on which is the most convenient to use. Amps have the advantage that this is the S.I. (International Standard) unit. This is convenient if you want to do any further processing becasue most formulae require values in S.I. For example, if you want to calculate power (in watts), you must multiply the current (amps) by the voltage (volts).
An alternative would be to state what the precision is for each range of measurements. Then you could get away with adding trailing zeros to the values in the results table.