6.6: §128. The Metric System
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)§128. The Metric System
The METRIC SYSTEM was developed in France during the decade that followed the French Revolution (1790-1799); the terminology was all drawn from Greek or Latin. The SYSTÈME INTERNATIONAL (SI) is a 20th century refinement and extension of metric, formally approved in 1960; its terminology goes beyond Greek and Latin. An excellent summary can be found in the Encyclopedia Britannica.
| Some original metric measures: | ||
| length | METRE | (< G μετρον): originally defined as “one ten-millionth part of a meridional quadrant of the earth” (the quadrant of the earth’s circumference running from the North Pole through Paris to the equator) |
| area | ARE | (< L area): 10 m x 10 m (= 100 m2) HECTARE (100 ares): 100 m x 100 m (= 10,000 m2) |
| mass | GRAM | (< Late L gramma, “small weight” < G γραμμα): 1 cc of distilled water at maximum density (4°C), weighed in vacuo |
| volume | LITRE | (< ML litra < G λιτρα, “a measure”): a cube 10 cm x 10 cm x 10 cm (1,000 cc); thus l litre of pure water has a mass of 1 kg |
| STERE | (< G στερεος): 1 cubic metre, or a cube 100 cm x 100 cm; thus 1 stere is equivalent to 1 kilolitre. | |
Prefixes in SI Measurement:
| Multiple | Prefix | Symbol | Etymology | |||
| trillion | 1012 | tera- | T | G | τερας | “monster” |
| billion | 109 | giga- | G | G | γιγας | “giant” |
| million | 106 | mega- | M | G | μεγας | “big” |
| thousand | 103 | kilo- | k | G | χιλιοι | |
| hundred | 102 | hecto- | h | G | ἑκατον | |
| ten | 10 | deka- | da | G | δεκα | |
| Submultiple | Prefix | Symbol | Etymology | |||
| tenth | 10-1 | deci- | d | L | decem | |
| hundredth | 10-2 | centi- | c | L | centum | |
| thousandth | 10-3 | milli- | m | L | mille | |
| millionth | 10-6 | micro- | μ | G | μικρος | small |
| billionth | 10-9 | nano- | n | G | νανος | dwarf |
| trillionth | 10-12 | pico- | p | It. | piccolo (?) | small |
| quadrillionth | 10-15 | femto- | f | Dan./Norw. | femten (15) | |
| quintillionth | 10-18 | atto- | a | Dan./Norw. | atten (18) | |