# Significant figures in standard and scientific notation

I know that standard notation can be changed into scientific notation and vice versa while preserving the number of significant figures, like $$100=1\times10^2$$ which has one significant figure, or $$100.=1.00\times10^2$$ has three sig figs.

Now this one seems problematic: $$1.0\times10^2$$ has two sig figs. What is the standard notation of $$1.0\times10^2$$ with two sig figs?

• "100" is ambiguous. THAT is why you should use scientific notation to indicate the significant figures in a number like this. Commented Jun 16, 2022 at 20:45
• Significant figures are a waste of time. One should just explicitly specify the magnitude of errors in all uncertain quantities. Commented Jun 16, 2022 at 21:02
• More on significant figures. Commented Jun 18, 2022 at 4:15

Now this one seems problematic: $$1.0\times10^2$$ has two sig figs. What is the standard notation of $$1.0\times10^2$$ with two sig figs?
Professional scientists today will simply report the actual uncertainty of any measurement. So we would write something like “$$100$$ with a standard uncertainty of $$3$$” or “$$100\pm 3$$” or “$$100(3)$$”. All of these make the situation clear and unambiguous. It also allows much more precise statements of the uncertainty.