Prefixs

From big to small

This is a short post on size and prefixes. Most things in physics are really large or really small. Number of atoms in a sugar cube, massive number. The charge on an electron, tiny number. Most of these numbers are so big, or small, as to have no real meaning, it is impossible for our brains to comprehend them.

Take the speed of light, 186,000 miles per second. Now the number 186,000 is well within our imagination, after all, that is about the average house price. One second in time is easily within our grasp, just look at the second hand on any clock. 186,000 miles per second though is too large for our brain to imagine.  1.3 seconds is the approximate time it takes light to travel from the moon to earth. But we have no real comprehension of the distance from here to the moon.

Many of us know what a meter looks like, or a centimeter or a millimeter, but then go to the next level, the micrometer, also called a micron. A micron is to small for the eye to see and to small for the brain to imagine.You can see things micron size using a microscope, but the image is then enlarged so it doesn't really count.

This problem of scale is true in many things and our range of experience is actually quiet small. The band of electromagnetic radiation that we can detect with our eye, that we call the visible spectrum, or visible light is very small. The frequency range is so high that once again it is beyond comprehension.

In a way things have started to change with the introduction of computers into every day life. Many people have GHz processors and GB of RAM. In hard drives these days we started out with mega byte disks that became gigabyte disks that became terabyte disks. Large storage facilities already deal in petabytes.

Many of use have heard of micro computers and nano technology. People are starting to recognize these terms as they are now part of every day experience. We may not understand properly what the terms mean, but we are starting at least to recognize the names.

So what is the difference between micro and nano? or the difference between a kilobyte, megabyte, gigabyte or terabyte?

Each step from kilo to mega to giga is a 1000 fold increase. Each step from milli to micro to nano is a 1000 fold decrease.


A mega is a thousand times bigger than a kilo, in the same way that a million is a thousand times bigger than a thousand. Similarly a gram is a thousand times smaller than a a kilogram. A milligram is a thousand times smaller than a gram, a microgram a thousand times smaller than a milligram.

Many people have heard of nano, micro, milli, kilo, mega, giga, Tera. That is a fair range, we have gone from 10^-9 to 10¹². That is 21 orders of magnitude (9+12 = 21). There are others, below we list those ranging from 10^-24 to 10²⁴. Some of them have some great names and using the naming conventions can be... interesting. Here are a few.

An electron has a charge of about 1.6x10^-19 Coulomb, this is 160 zepto Coulombs or 160 Trilliardths of a Coulomb.

The mass of the earth is about 6 x 10²⁴kg, or 6 yotta kilograms or 6 Septillion kilograms. 

1 light year, the distance you would go in 1 year if you were travelling at the speed of light, is approximately 10¹⁶meters which is 10 peta meters or 10Pm, or 10 Billiard meters.

Here is a list going from the very big to the very small. I think you will surprised by how many you have heard of.

Prefix	Symbol	1000m	10n	Decimal	Short scale	Long scale	Since[n 1]
yotta	Y	10008	1024	1000000000000000000000000	Septillion	Quadrillion	1991
zetta	Z	10007	1021	1000000000000000000000	Sextillion	Trilliard	1991
exa	E	10006	1018	1000000000000000000	Quintillion	Trillion	1975
peta	P	10005	1015	1000000000000000	Quadrillion	Billiard	1975
tera	T	10004	1012	1000000000000	Trillion	Billion	1960
giga	G	10003	109	1000000000	Billion	Milliard	1960
mega	M	10002	106	1000000	Million		1960
kilo	k	10001	103	1000	Thousand		1795
hecto	h	10002/3	102	100	Hundred		1795
deca	da	10001/3	101	10	Ten		1795
		10000	100	1	One		–
deci	d	1000−1/3	10−1	0.1	Tenth		1795
centi	c	1000−2/3	10−2	0.01	Hundredth		1795
milli	m	1000−1	10−3	0.001	Thousandth		1795
micro	μ	1000−2	10−6	0.000001	Millionth		1960
nano	n	1000−3	10−9	0.000000001	Billionth	Milliardth	1960
pico	p	1000−4	10−12	0.000000000001	Trillionth	Billionth	1960
femto	f	1000−5	10−15	0.000000000000001	Quadrillionth	Billiardth	1964
atto	a	1000−6	10−18	0.000000000000000001	Quintillionth	Trillionth	1964
zepto	z	1000−7	10−21	0.000000000000000000001	Sextillionth	Trilliardth	1991
yocto	y	1000−8	10−24	0.000000000000000000000001	Septillionth	Quadrillionth	1991
The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the General Conference on Weights and Measures.

There are some numbers in physics that are outside of the ranges given above. The mass of an electron is approximately10^-30kg, which is,  hmmm, a micro yocto or is it a yocto micro?  ... think I need to take another at my scale.


When a tera byte hard drive isn't.... 

The definition of a kilobyte needs clarity, see a kilobyte is 1024 bytes but in physics a kilo is 1000. So in computer speak kilo means 1024, in physics it is 1000. This has allowed hard drive creators to pull a little trick, and steal 9% of your Tera byte hard drive. Here is how they do it.

In computer speak a hard drive size is measured in kilobytes, megabytes and so on. A kilobyte is 1024 bytes

1024 = 2¹⁰ =2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

but in physics a kilo is 1000.Hard drive manufacturers use physics notation rather than computer notation, so,

A 1 terabyte hard drive = 1000 gigabytes = 1,000,000 mega bytes = 1,000,000,000 kilo bytes, which is a large number,

1 Tera byte = 1,000,000,000,000 or 10¹² bytes

but if we used the computer definition then

1 Tera byte = 1024 gigabytes = 1,048,576 mega bytes = 1,073,741,824 kilo bytes

1 Tera byte = 1,099,511,627,776, an even larger number!

So by using physics notation rather than computer notation, hard drive manufacturers have managed to skim 9% of the size of a drive. Our 1TB drive is actually missing 99,511,627,776 bytes, which is about 92GB! So a 1TB hard drive is really a 0.909TB hard drive or 932GB.

92GB + 932GB = 1024GB,

which is the proper definition of a terabyte, in computing. This is why your new shiny 2 TB hard drive shows up as 1.818TB as soon as you load it into your computer!