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There are 3 orders of magnitude between nano (^-9) and pico (^-12). An Angstrom is ^-10m.
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Useless fact I just learned from Wikipedia: Ångström/Angstrom (in Sweden of course we still use the original spelling) has its own UNICODE symbol, Angstrom sign: Å (U+212B) not to confuse with the Swedish letter Å (U+00C5). Looks slightly different in my browser.

https://en.wikipedia.org/wiki/Angstrom

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Looks like that's deprecated. From the next sentence:

However, version 5 of the standard already deprecates that code point and has it normalized into the code for the Swedish letter U+00C5 Å `latin capital letter a with ring above`

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Aaahhh, ok, thanks!
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You had the right idea. Angstroms are not an SI unit. The SI units jump by three orders of magnitude at this scale: picometer, nanometer, micrometer, millimeter.

(In the same way that meter jumps three orders of magnitude to kilometer[1], or millions to billions to trillions, etc.)

[1] Technically there are intermediate SI units between meter and km but nobody uses them. There are not intermediate SI units between the tiny ones.

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Why above 1mm do we go by tens instead of thousands?

We have centimeter (10 mm) then decimeter (100mm) then meter (1000mm). Then we jump to thousand again (kilometer).

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>We have centimeter (10 mm) then decimeter (100mm)

Does anyone actually use those? I think I would throw up a little in my mouth if I saw either of those on a mechanical drawing.

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Answer that question and you'll get the whole impetus for logarithmic scales.
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Everyday necessity. The gap between mm and m is too large, there are many things in daily life that are better expressed in cm. SI units must strike a balance between three factors: not having so many denominations nobody can remember them; not having so few denominations that using them adds too much wordiness to daily life (150mm or 0.15m are wordier than 15cm); and a degree of familiarity with the everyday units people used before metric, to smooth the transition and encourage adoption.
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Because 1 angstrom equals 10⁻¹⁰ meters and 1 picometer equals 10⁻¹² meters, the relationship is:

1 Å = 100 pm. 1 pm = 0.01 Å.

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1 picometer = 0.001 nanometers, 0.01 angstrom

1 angstrom = 0.1 nanometers, 100 picometers

1 nanometer = 10 angstroms, 1000 picometers

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