#import "../../core/core.typ"

=== Metric notation

The metric system, besides being a collection of measurement units for
all sorts of physical quantities, is structured around the concept of
scientific notation. The primary difference is that the powers-of-ten
are represented with alphabetical prefixes instead of by literal
powers-of-ten. The following number line shows some of the more common
prefixes and their respective powers-of-ten:

#image("static/00356.png")

Looking at this scale, we can see that 2.5 Gigabytes would mean $2.5 times 10^9 "bytes"$,
or 2.5 billion bytes. Likewise, 3.21 picoamps would
mean $3.21 times 10^-12 "amps"$, or $3.21 1/"trillionths of an amp"$.

Other metric prefixes exist to symbolize powers of ten for extremely
small and extremely large multipliers. On the extremely small end of the
spectrum, $"femto"(f) = 10^-15$, $"atto"(a) = 10^-18$,
$"zepto"(z) = 10^-21$, and $"yocto"(y) = 10^-24$. 
On the extremely large end of the spectrum,
$"Peta"(P) = 10^15$, $"Exa"(E) = 10^18$,
$"Zetta"(Z) = 10^21$, and $"Yotta"(Y) = 10^24$.

Because the major prefixes in the metric system refer to powers of 10
that are multiples of 3 (from \"kilo\" on up, and from \"milli\" on
down), metric notation differs from regular scientific notation in that
the significant digits can be anywhere between 1 and 1000, depending on
which prefix is chosen. For example, if a laboratory sample weighs
0.000267 grams, scientific notation and metric notation would express it
differently:

$ 2.67 times 10^-4 "grams (scientific notation)" $

$ 267 "µgrams (metric notation)" $

The same figure may also be expressed as 0.267 milligrams (0.267 mg),
although it is usually more common to see the significant digits
represented as a figure greater than 1.

In recent years a new style of metric notation for electric quantities
has emerged which seeks to avoid the use of the decimal point. Since
decimal points (\".\") are easily misread and/or \"lost\" due to poor
print quality, quantities such as 4.7 k may be mistaken for 47 k. The
new notation replaces the decimal point with the metric prefix
character, so that \"4.7 k\" is printed instead as \"4k7\". Our last
figure from the prior example, \"0.267 m\", would be expressed in the
new notation as \"0m267\".


#core.review[
  - The metric system of notation uses alphabetical prefixes to represent
    certain powers-of-ten instead of the lengthier scientific notation.
]
