Testwiki:Reference desk/Archives/Mathematics/2014 March 28

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March 28

1 x 10¹¹

I found the number "1 x 10¹¹" ; my question is, how is it different from "10¹¹" and "1.0 x 10¹¹" ?

• I think 10¹¹ is the exact number 100,000,000,000.
• I'm sure that 1.0 x 10¹¹ indicates more significant figures than 1 x 10¹¹. 1.0 x 10¹¹ has an uncertainty of 0.05 x 10¹¹, it is between 95 billion and 105 billion.
• 1 x 10¹¹ is between 95 billion (closer to 100,000,000,000 than to 9 x 10¹⁰ = 90,000,000,000) and 150 billion (closer to 100,000,000,000 than 2 x 10¹¹ = 200,000,000,000).

Is that usage/interpretation, esp. the latter, correct? - ¡Ouch! (^{hurt me} / _{more pain}) 07:21, 28 March 2014 (UTC)

This all seems consistent with Significant_digits#Scientific_notation. But really, this stuff can be context dependent, and there may be different customs of notation used by different authors. If we cant to be clear, we can always just use explicit plus or minus symbols, e.g. $10^{11}\pm 500$, rather than writing out $1.000000000\times 10^{11}$ to make use of a convention. SemanticMantis (talk) 15:27, 28 March 2014 (UTC)

The bands on either side due to limited precision are usually symmetrical, so on that basis 1 x 10¹¹ would be between 50 billion and 150 billion.→86.173.216.149 (talk) 19:11, 28 March 2014 (UTC)