Converting nanometres and microns to millimetres

[Cliff Hanley]

Have I got the following correct;

1 micron = 1 micrometre

1 micrometre = 1 millionth of a metre

= 10^-6m

To convert m to mm we multiply m by 1000, eg, 1 m = 1 x 1000 therefore 1 m = 1000mm; 1000m = 10^6mm.

Therefore 1 micron = 10^-3mm (one millionth of a metre = one thousandth of a millimetre) ?

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1 nanometre (nm) = 1 billionth of a metre = 10^-9m

To convert m to mm we multiply be 1000

Therefore 10^9m = 10^6mm (one billionth of a metre = one millionth a metre)

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I am profoundly moved to learn that a mm can be divided into a thousand parts (a micron); and even more so that it can be divivded into a million parts (a nm). That’s assuming I’ve understood this correctly.

 

[Mentallic]

Have I got the following correct;

1 micron = 1 micrometre

1 micrometre = 1 millionth of a metre

= 10^-6m

To convert m to mm we multiply m by 1000, eg, 1 m = 1 x 1000 therefore 1 m = 1000mm; 1000m = 10^6mm.

Therefore 1 micron = 10^-3mm (one millionth of a metre = one thousandth of a millimetre) ?

Good so far.

*

1 nanometre (nm) = 1 billionth of a metre = 10^-9m

To convert m to mm we multiply be 1000

Therefore 10^9m = 10^6mm (one billionth of a metre = one millionth a metre)

What you've just written is 1 billion metres = 1 million millimetres. Does that sound right to you?

You need to understand what the phrase "To convert m to mm we multiply be 1000" actually means. When we say this, we mean that we want to turn the value in metres into a value in millimetres. We go from m -> mm. We know that a factor of 1000 is involved between them, and that the mm is smaller than the m, so we need 1000mm = 1m.
If you ever aren't sure of where the 1000 or bigger number goes, just think which unit of measurement (m or mm for example) is smaller, because you always need more of those.

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I am profoundly moved to learn that a mm can be divided into a thousand parts (a micron); and even more so that it can be divivded into a million parts (a nm). That’s assuming I’ve understood this correctly.

Yes, and it keeps going from there with picometres, then femtometres, attometres etc. You can read about it on wikipedia:

https://en.wikipedia.org/wiki/Orders_of_magnitude_(length)

 

[mfb]

All multiplications you do should be multiplications by 1. That's the only factor that won't change your value.

You can express "1" in a clever way, however, for example as $1=\frac{1000mm}{1m}$. That is true as 1000mm = 1m.

To convert something like 4.5 m from meters to millimeters, just multiply by 1 (here done in more detail than necessary):
$$ 4.5 m = 4.5 m \cdot 1 = 4.5 m \frac{1000mm}{1m} = \frac{4.5 m \cdot 1000mm}{1m} = 4500 mm$$
as the meter cancels.

 

[Fredrik]

It works out quite well to treat notations like "m" and "mm" the same way you would treat variables that represent numbers. For example

\begin{align*}
&\mathrm{km}=10^3\,\mathrm{m},\qquad \mathrm m=10^{-3}\,\mathrm{km}\\
&\mathrm h=3600\,\mathrm s,\qquad \mathrm s=\frac{\mathrm h}{3600}\\
& 10\, \mathrm m/\mathrm s =\frac{10\mathrm m}{\mathrm s} =\frac{10\cdot(10^{-3}\mathrm{km})}{\frac{\mathrm h}{3600}} =(10\cdot 10^{-3})\mathrm{km}\frac{3600}{\mathrm h} =\frac{36\,\mathrm{km}}{\mathrm h} =36\,\mathrm{km}/\mathrm h.
\end{align*}