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MATHSKIT

How precise can you be?

David Swinscoe explains why numbers in physics are written down in the precise way that they are

© Daisy Daisy/stock.adobe.com

When you are given a calculation question in physics, the numbers are sometimes presented in a way that may be surprising. You could be asked to calculate the speed of an object that has travelled 17 m in 7.0 s. The decimal place in the 7.0 s looks a little unnecessary. What is the difference between 7.0 s and 7 s?

When we see 7.0 s it tells us something about how precisely we know how much time has passed. It suggests that we know the length of time is precise to about one decimal place — perhaps the timer only shows one decimal place. If the time was rounded to the nearest tenth of a second, it could be somewhere between 6.95 s and 7.05 s. However, if we write 7 s it suggests that we are less precise about the amount of time that has passed. If the time was rounded to the nearest whole second, it could be between 6.5 s and 7.5 s.

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Vera Rubin 1928–2016

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