round the measurement of two significant numbers

Chemistry
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182.0448L

Aug 22nd, 2015

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The different versions have different numbers of digits and extend to different numbers of decimal places, but they all represent the same measurement with the same uncertainty.  We conclude from this that a number's precision -- its random error -- is not indicated by the number of digits or by the number of decimal places.

The versions in the fourth and fifth columns, expressed in scientific notation, make it clear that only the three digits "208" tell you anything about precision.  All other digits in the first three columns are unnecessary leading zeros (0.208 m), leading zeros which tell you where the decimal point goes (.000208 km), and trailing zeros which tell you where the ones place is (208000 ┬Ám).

Just what do the digits "208" tell us about the number's precision?  They tell us that the random uncertainty is a few parts in 208 -- that is, roughly a part in 100, or 1%.  The larger the number of "significant digits" (or "significant figures"), the finer the precision.  By using the correct number of significant figures, we let the world know just how reliable our measurements are.


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Aug 22nd, 2015

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