approximately, about, some (degree of formality)

[herbivorie]

I know "approximately" is more formal than "about".
How about "some" when it's used to mean the same thing?

1. There are about 13 million people in Tokyo.
2. There are approximately 13 million people in Tokyo.
3. There are some 13 million people in Tokyo.

Is 3 more formal than others, or less formal than others?

 

[tedmc]

'About' is most commonly used.
'Approximately', which connotes degree of accuracy, is widely used in scientific/technological writing.
'Some' is less common, not really more formal and tends to be used more in narratives.
'Roughly' would be less formal.

The above are from my personal observation.

not a teacher

 

[MikeNewYork]

For me, "formality" is often in the eyes of the beholder. All three of your sentences work.

 

[herbivorie]

Is "some" (in this sense) used in formal documents such as product manuals or scientific papers?

 

[Rover_KE]

Any of the three alternatives might be found in the documents you specify.

 

[SoothingDave]

I would not expect to see "some" used in this sense in a product manual or specification sheet, etc.