= Decimetre
{title2=$\mathrm{dm}$}
A \b[decimetre], symbol $\mathrm{dm}$, is exactly one tenth of a <metre>:
$$
1\,\mathrm{dm}=10^{-1}\,\mathrm m=10\,\mathrm{cm}=100\,\mathrm{mm}.
$$
The SI prefix deci fixes the factor $10^{-1}$. This exact relation concerns units; the uncertainty of a measured <length> still depends on the measurement.<The International System of Units (SI), ninth edition, SI Brochure>[Chapter 3, Table 7: deci prefix and factor; chapter 2: metre.]{ref}
The <decimetre> connects familiar lengths to <volume> particularly neatly. A cube with edges $1\,\mathrm{dm}$ has <volume>
$$
(1\,\mathrm{dm})^3=(10^{-1}\,\mathrm m)^3=10^{-3}\,\mathrm{m^3}=1\,\mathrm L.
$$
Thus a <litre> is exactly a cubic <decimetre>, while a cubic <metre> contains 1,000 <litres>. The exponent acts on the conversion factor as well as the unit: a cubic <decimetre> is not one tenth of a cubic <metre>.<The International System of Units (SI), ninth edition, SI Brochure>[Chapter 4, Table 8 note d: litre equals cubic decimetre.]{ref}
For example, a rectangular container measuring $2\,\mathrm{dm}$ by $3\,\mathrm{dm}$ by $0.5\,\mathrm{dm}$ has <volume> $3\,\mathrm{dm^3}=3\,\mathrm L$, assuming the stated dimensions describe its interior. A length conversion becomes a cubic conversion when used to compute <volume>.
Back to article page
