# What does “as small as a fraction of an angstrom” mean?

I was reading my school textbook in which the following statement was given:

The resolution of such an electron microscope is limited finally by the fact that electrons can also behave as waves! (You will learn more about this in class XII). The wavelength of an electron can be as small as a fraction of an angstrom.

What does the highlighted statement mean?

Does it mean $1 \:\mathrm{angstrom}/100$?

Or $1\:\mathrm{angstrom}/1\:\mathrm{angstrom}$?

Basically, I just want to know how will the above statement can be represented mathematically?

• This appears to be less a question about physics and more about the English language: "as small as a fraction of an X" means effectively the same as "smaller than an X". – ACuriousMind Aug 25 '18 at 11:02
• How will write it mathematically? 10^-20 angstrom? – Saksham Sharma Aug 25 '18 at 11:04
• It is spelled ångström. – Qmechanic Aug 25 '18 at 11:09
• @SakshamSharma Well, you'd write it as $10^{-20} Å$ and it is certainly is a fraction of an angstrom. And no, "1 Angstrom/1Angstrom" doesn't make any sense. – Blue Aug 25 '18 at 11:10
• – jinawee Aug 25 '18 at 14:38

In essence, what it's conveying is that the wavelength $\lambda$ in question can be smaller than 1 angstrom, $$\lambda < 1 \: Å.$$ However, it does not really specify how much smaller that wavelength will be. Typically you'd use that language for situations in which $\lambda \approx 0.1 \: Å$ is achievable, going down to maybe things like $\lambda \approx 0.001 \: Å$, but the further down you get, the less applicable that language becomes (so, say, something like $\lambda \approx 10^{-20} \: Å$ would not be included in that usage, as it's just too small). Since the construction is fuzzy, though, there is no hard bottom at which the length is too small to qualify.
And as for the fraction $1\: Å/1 \: Å$, that is a dimensionless number and not a length, so a wavelength cannot be equal to that.