Thank you for the opportunity to help you with your question!
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 µm).
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.
Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 22nd, 2015
Did you know? You can earn $20 for every friend you invite to Studypool!