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The inch is an imperial unit of length.

\(\displaystyle \) \(\) \(\displaystyle 1\) inch
\(\displaystyle \) \(=\) \(\displaystyle 2 \cdotp 54\) centimetres
\(\displaystyle \) \(=\) \(\displaystyle 0 \cdotp 0254\) metres

This definition is exact, and is how the imperial unit of length is defined.

Linguistic Note

The word inch derives ultimately from the same root as ounce, that is, from the Latin word uncia, meaning $\dfrac 1 {12}$ part.

In this context, the inch is of course the $\dfrac 1 {12}$ part of a foot.

From the same root, the uncial letters of a mediaeval manuscript are letters which are an inch high.

Despite the gradual migration to the metric system, the word inch still lives on as a rhetorical flourish for a small distance, for example:

Slowly and steadily they inched forward ...
Give him an inch and he'll take a mile.