2.2: Introduction to the Metric System
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- 53532
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Introduction to the Metric System
Scientific measurements use the metric system - a system of measurement used worldwide that is very user-friendly since the units of measurement differ by magnitudes of 10. Since microscopes are concerned with the size (length) of structures and the magnification of these structures, we will consider the metric system as it relates to length. The base unit of length in the metric system is the meter (abbreviated as m). One meter is about 3.3 feet long. For units that are larger or smaller than meters, a prefix is added to the beginning of "meter" to indicate the magnitude of difference from the meter unit (base unit):
|
Prefix Name |
Prefix Symbol |
Size in relationship to the base unit (base unit =1) |
|---|---|---|
|
kilo- |
k |
1,000 |
|
hecto- |
h |
100 |
|
deca- |
da |
10 |
|
base unit |
none |
1 |
|
deci- |
d |
0.1 |
|
centi- |
c |
0.01 |
|
milli- |
m |
0.001 |
|
micro- |
µ |
0.000001 |
|
nano- |
n |
0.000000001 |
|
pico- |
p |
0.000000000001 |
Using the table above that distinguishes units by prefix, to convert unit measurements back to the base unit, simply multiply the number you are converting with the number in the "size relationship to the base unit" column. For example:
Using your microscope you measure a cell as 20 µm ("twenty micrometers"). To convert 20 µm to meters, multiply 20 µm by 0.000001:
20 µm x 0.000001 = 0.00002 m
You measure the distance it takes you to get home from school as 19 km ("nineteen kilometers"). To convert 19 km to meters, multiply 19 km by 1,000:
19 km x 1,000 = 19,000 m
Using the table above that distinguishes units by prefix, to convert the base unit to another unit, simply divide the number you are converting with the number in the "size relationship to the base unit" column. For example:
You are told that a certain very large cell is 0.0003 m long. To convert 0.0003 m to micrometers (µm), divide 0.0003 m by 0.000001:
0.0003 m ÷ 0.000001 = 300 µm
You read that running a marathon means running 42,000 m. To convert 42,000 m to kilometers (km), divide 42,000 m by 1,000:
42,000 m ÷ 1,000 = 42 km
Cells are typically measured using the micrometer (µm) unit, but some subcellular structures may be reported in nanometers (nm) measurements. To give you a sense of cell size, a typical human red blood cell is about eight millionths of a meter or eight micrometers (abbreviated as 8 μm) in diameter; the head of a pin of is about two thousandths of a meter (two mm) in diameter. That means about 250 red blood cells could fit on the head of a pin!
Check out this slider tool to get a sense of how big cells and cellular structures are in comparison to some familiar objects: http://learn.genetics.utah.edu/content/cells/scale/
Attribution
- "Biology 2e" by Mary Ann Clark, Matthew Douglas, Jung Choi, OpenStax is licensed under CC BY-NC 4.0