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# Why use a certain number of significant figures? watch

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1. Why would you use, for example, 3 s.f. instead of 2 or 4?

And what does precision and accuracy mean?

Any help appreciated.
2. You use 3 signisifcant figures generally to show you're quite sure your asnwer is correct ut you arnt ery very sure which 4 significant figures would suggest. Accuracy are results which are close to the truve value, and precision is how precise the instrument can measure like the smallst scale devisions.
3. Consider human reaction times. Typically to 2 s.f. Anything beyond that is highly unrealistic for us.

Try it yourself, grab yourself a stop watch and see how fast you can start/stop the clock. I think the fastest human reaction time is around 0.30 seconds. Not sure.
4. Well in general if we're given data/information and we're asked to calculate new information, there isn't really any point of quoting to a greater number of significant figures than the data provides, so if all the given information (e.g. in an experiment) is written to 2 s.f. then you must also give your calculated new information to 2 s.f. to be consistent.
5. The number of significant figures in data is one way of expressing the precision of that data. This is just one way of expressing how confident you are in the value. In this case, precision is about the smallest change in the value you can measure or express. With measuring instruments*, precision is usually determined by the smallest graduation on the scale.
Accuracy is more about how near to the "correct" value a measurement is.
Significant figures is mostly used in physics questions when providing you with data. For example, the acceleration due to gravity in a problem could be given as (in m/s/s):

9.81 (3 sig figs)
9.8 (2 sig figs0
10 (1 sig fig)

If the value is given to 3 sig figs then normally other data will (should!) be given to the same number.
Similarly, and importantly, your answer would be given to the same number.

*In practical physics, the precision and/or accuracy of measurements (often called uncertainty) is given as a ± value rather than using significant figures.
Eg. I measured the current in the wire to be 1.35 ± 0.02 A
6. Thanks.

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