Definition:Metric System/Length

From ProofWiki
Jump to navigation Jump to search

Definition

Various metric units of length which have specific names are as follows:

Angstrom

The angstrom is a metric unit of length.


\(\ds \) \(\) \(\ds 1\) angstrom
\(\ds \) \(=\) \(\ds 10^{-1}\) nanometres
\(\ds \) \(=\) \(\ds 10^{-4}\) micrometres
\(\ds \) \(=\) \(\ds 10^{-7}\) millimetres
\(\ds \) \(=\) \(\ds 10^{-8}\) centimetres
\(\ds \) \(=\) \(\ds 10^{-10}\) metres


Nanometre

The nanometre is a metric unit of length.

\(\ds \) \(\) \(\ds 1\) nanometre
\(\ds \) \(=\) \(\ds 10\) angstroms
\(\ds \) \(=\) \(\ds 10^{-3}\) micrometre
\(\ds \) \(=\) \(\ds 10^{-6}\) millimetre
\(\ds \) \(=\) \(\ds 10^{-9}\) metres


Micrometre

The micrometre is a metric unit of length.


\(\ds \) \(\) \(\ds 1\) micrometre
\(\ds \) \(=\) \(\ds 10^{-3}\) millimetre
\(\ds \) \(=\) \(\ds 10^{-6}\) metres
\(\ds \) \(=\) \(\ds 39 \cdotp 3708\) microinches


Millimetre

The millimetre is a metric unit of length.

\(\ds \) \(\) \(\ds 1\) millimetre
\(\ds \) \(=\) \(\ds 1 \, 000 \, 000\) nanometres
\(\ds \) \(=\) \(\ds 1000\) micrometres
\(\ds \) \(=\) \(\ds 10^{-3}\) metres


Centimetre

The centimetre is the CGS base unit of length.

\(\ds \) \(\) \(\ds 1\) centimetre
\(\ds \) \(=\) \(\ds 10\) millimetres
\(\ds \) \(=\) \(\ds 10 \, 000\) micrometres
\(\ds \) \(=\) \(\ds 0 \cdotp 01\) metre
\(\ds \) \(=\) \(\ds 0 \cdotp 39370 \, 8\) inch
\(\ds \) \(=\) \(\ds 0 \cdotp 0328\) foot
\(\ds \) \(=\) \(\ds 0 \cdotp 0109\) yard


Decimetre

The decimetre is a metric unit of length.

\(\ds \) \(\) \(\ds 1\) decimetre
\(\ds \) \(=\) \(\ds 10\) centimetres
\(\ds \) \(=\) \(\ds 100\) millimetres
\(\ds \) \(=\) \(\ds 0 \cdotp 1\) metres


Metre

The metre is the SI base unit of length.

It is defined as the distance travelled by light in vacuum in $\dfrac 1 {299 \ 792 \ 458}$ of a second.

\(\ds \) \(\) \(\ds 1\) metre
\(\ds \) \(=\) \(\ds 100\) centimetres
\(\ds \) \(=\) \(\ds 1000\) millimetres
\(\ds \) \(=\) \(\ds 1 \, 000 \, 000\) micrometres
\(\ds \) \(=\) \(\ds 39 \cdotp 3708\) inches
\(\ds \) \(=\) \(\ds 3 \cdotp 28\) feet
\(\ds \) \(=\) \(\ds 1 \cdotp 09\) yards


Hectometre

The hectometre is a metric unit of length.

\(\ds \) \(\) \(\ds 1\) hectometre
\(\ds \) \(=\) \(\ds 100\) metres
\(\ds \) \(=\) \(\ds 10 \, 000\) centimetres
\(\ds \) \(=\) \(\ds 100 \, 000\) millimetres


Kilometre

The kilometre is a metric unit of length.

\(\ds \) \(\) \(\ds 1\) kilometre
\(\ds \) \(=\) \(\ds 10\) hectometres
\(\ds \) \(=\) \(\ds 100\) dekametres
\(\ds \) \(=\) \(\ds 1000\) metres
\(\ds \) \(=\) \(\ds 100 \, 000\) centimetres
\(\ds \) \(=\) \(\ds 10^6\) millimetres
\(\ds \) \(=\) \(\ds 39 \, 370 \cdotp 4\) inches
\(\ds \) \(=\) \(\ds 0.621\) miles