2.1.2: Prefixes
- Page ID
- 370141
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Learning Objectives
- Describe how prefixes are used in the metric system and identify how the prefixes milli-, centi-, and kilo- compare to the base unit.
- To express a large number or a small number in scientific notation
Prefix Multipliers
Conversions between metric system units are straightforward because the system is based on powers of ten. For example, meters, centimeters, and millimeters are all metric units of length. There are 10 millimeters in 1 centimeter and 100 centimeters in 1 meter. Metric prefixes are used to distinguish between units of different size. These prefixes all derive from either Latin or Greek terms. For example, mega comes from the Greek word \(\mu \varepsilon \gamma \alpha \varsigma\), meaning "great". Table \(\PageIndex{2}\) lists the most common metric prefixes and their relationship to the central unit that has no prefix. Length is used as an example to demonstrate the relative size of each prefixed unit.
| Prefix | Unit Abbreviation | Meaning | Example |
|---|---|---|---|
| giga | \(\text{G}\) | 1,000,000,000 | 1 gigameter \(\left( \text{Gm} \right)=10^9 \: \text{m}\) |
| mega | \(\text{M}\) | 1,000,000 | 1 megameter \(\left( \text{Mm} \right)=10^6 \: \text{m}\) |
| kilo | \(\text{k}\) | 1,000 | 1 kilometer \(\left( \text{km} \right)=1,000 \: \text{m}\) |
| hecto | \(\text{h}\) | 100 | 1 hectometer \(\left( \text{hm} \right)=100 \: \text{m}\) |
| deka | \(\text{da}\) | 10 | 1 dekameter \(\left( \text{dam} \right)=10 \: \text{m}\) |
| 1 | 1 meter \(\left( \text{m} \right)\) | ||
| deci | \(\text{d}\) | 1/10 | 1 decimeter \(\left( \text{dm} \right)=0.1 \: \text{m}\) |
| centi | \(\text{c}\) | 1/100 | 1 centimeter \(\left( \text{cm} \right)=0.01 \: \text{m}\) |
| milli | \(\text{m}\) | 1/1,000 | 1 millimeter \(\left( \text{mm} \right)=0.001 \: \text{m}\) |
| micro | \(\mu\) | 1/1,000,000 | 1 micrometer \(\left( \mu \text{m} \right)=10^{-6} \: \text{m}\) |
| nano | \(\text{n}\) | 1/1,000,000,000 | 1 nanometer \(\left( \text{nm} \right)=10^{-9} \: \text{m}\) |
| pico | \(\text{p}\) | 1/1,000,000,000,000 | 1 picometer \(\left( \text{pm} \right)=10^{-12} \: \text{m}\) |
There are a couple of odd little practices with the use of metric abbreviations. Most abbreviations are lowercase. We use "\(\text{m}\)" for meter and not "\(\text{M}\)". However, when it comes to volume, the base unit "liter" is abbreviated as "\(\text{L}\)" and not "\(\text{l}\)". So we would write 3.5 milliliters as \(3.5 \: \text{mL}\).
As a practical matter, whenever possible you should express the units in a small and manageable number. If you are measuring the weight of a material that weighs \(6.5 \: \text{kg}\), this is easier than saying it weighs \(6500 \: \text{g}\) or \(0.65 \: \text{dag}\). All three are correct, but the \(\text{kg}\) units in this case make for a small and easily managed number. However, if a specific problem needs grams instead of kilograms, go with the grams for consistency.
Example \(\PageIndex{2}\): Unit Abbreviations
Give the abbreviation for each unit and define the abbreviation in terms of the base unit.
- kiloliter
- microsecond
- decimeter
- nanogram
Solutions
| Explanation | Answer | |
|---|---|---|
| a | The prefix kilo means “1,000 ×,” so 1 kL equals 1,000 L | kL |
| b | The prefix micro implies 1/1,000,000th of a unit, so 1 µs equals 0.000001 s. | µs |
| c | The prefix deci means 1/10th, so 1 dm equals 0.1 m. | dm |
| d | The prefix nano means 1/1000000000, so a nanogram is equal to 0.000000001 g | ng |
Exercise \(\PageIndex{2}\)
Give the abbreviation for each unit and define the abbreviation in terms of the base unit.
- kilometer
- milligram
- nanosecond
- centiliter
- Answer a
- km
- Answer b
- mg
- Answer c
- ns
- Answer d
- cL
| \( 4.7\times 10^{-31}\) |
Summary
- Metric prefixes derive from Latin or Greek terms. The prefixes are used to make the units manageable.
Contributions & Attributions
This page was constructed from content via the following contributor(s) and edited (topically or extensively) by the LibreTexts development team to meet platform style, presentation, and quality:
Henry Agnew (UC Davis)