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Will my numbers add up correctly if I round them?

Published online by Cambridge University Press:  17 October 2016

David Hopkins
David Hopkins*
Affiliation:
27 Byron Mews, London NW3 2NQ e-mail: david.k.hopkins@blueyonder.co.uk
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Extract

I recently wrote a solution to a student problem. The answers were the probabilities for four possible outcomes. As a check on the calculations, I wanted to say ‘As expected, these probabilities add up to 1.’ However, they didn't! Because of rounding, the probabilities (which I was quoting to four decimal places) only added up to 0.9999. To rescue the situation I tried rounding to 3DP or 5DP instead, but these didn't add up correctly either.

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Articles
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The Mathematical Gazette , Volume 100 , Issue 549 , November 2016 , pp. 396 - 409
Copyright
Copyright © Mathematical Association 2016 

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References

1. Trainin, J., Integrating expressions of the form and others, Math. Gaz. 94 (July 2010) pp. 216–233.CrossRefGoogle Scholar
2. Poundstone, William, How to predict the unpredictable, Oneworld Publications (2014), Chapter 10.Google Scholar
3. Nelsen, Roger B. & James E. Schultz, , The probability that the ‘sum of the rounds’ equals the ‘round of the sum’, The College Mathematics Journal 18 (5) (November 1987), pp. 390–396, also available at http://www.jstor.org/stable/i326534 Google Scholar
4. Nahin, Paul J., Inside interesting integrals, Springer (2015), Section 7.7.CrossRefGoogle Scholar