I agree with Bob's opinion. But that's not the point or purpose of this thread.
Since we are talking about scientific notation, shouldn't the conversion be carried out with a "physical (measurement) sense" in mind, even if it is to be done in a math quiz? I've read somewhere that ambiguity can be avoided in at least one scenario: Write 255,000 if 3 significant digits is intended. Write 255,000. (with a trailing decimal point) if 6 significant digits is intended. What are we to do (in a nonclumsy way) if we intend something in between?
In a message dated 8/17/2009 8:02:47 A.M. Eastern Daylight Time, firstname.lastname@example.org writes:
I would say that in a mathematical sense, your friend is right. In a physical (measurement) sense, you are right. It is hard to talk about precision without some context.
For example, 255,000 might only have 3 digits of precision. You really don't know how many digits of precision that number has because it wasn't indicated (which is an advantage of scientific notation). Generally, they would indicate the precision separately if they are just using standard notation.
But you are correct to say that a number written as 2.55000 * 10^5 has 6 digits of precision.