Orders of Magnitude
The applet, called "the powers of ten" shows the "orders of magnitude" of the "size scale." ( You must click on blue c4a above to call it).
As in all knols , clicking on a small picture (a thumbnail) will enlarge it. And when you click on the blue "c4a" ("click for applet"), you get more than a larger picture. You get an small application (app-let), which allows you explore the pictured concept interactively. And aclick on blue c4s brings the source of the picture.
The icon above shows a frame E7 meters across, almost enough to contain the entire Earth, which has a diameter of 1.2E7 meters.
Now to the heart of the matter: What is this "E number"? E7, E20, even E with a negative number?
The E stands for "exponent." E5 is just a different way of writing 10^5 or 105, which is 10 to power of 5 = 10*10*10*10*10= 100000 (one hundred thousand). Thus E5 m is one hundred thousand meters. The Earth's diameter is about 12 million meters or, written elegantly: 12E6m.
Similarly E -1 is 10 ^( -1) = 1/10 = one tenth. Thus E-1 m is 10 centimeters, the size of a leaf.
In this knol we demonstrate some handy tricks which this way of writing numbers allows us.
Like this one: Just add the exponents
Finding the answer is easy:
total= 1000 * 1000000 = 1000000000 ,
but it is even easier when we write it like this:
total= E3 * E6 = E9 The answer, 1 followed by 9 zeros is called a billion in the U.S. and a milliard in most of the EU. Not always, however. Cross-culturally and therefore globally, names for numbers such as billion, trillion, .. can be so hopelesly ambiguous that it is best to avoid them altogether.Writing a number 3456.7 as 3.4567E3 is writing that number in scientific notation.
Adding E3 effectively shifts the decimal point 3 places to the left:
3000.00 = 3.00E3
Adding E-2 effectively shifts the decimal point 2 places to the right.
.003 = .3E-2 = 3.00E-3 = 30.00E-4 etc.
That is so, because E1 means "multitply by 10", E2 "multitply by 100" etc.
How much energy do "we all" use every second?
Now, let's apply this compact way of writing numbers, the scientific notation, to a real planet, our Earth, where the population is 6.7 E9 people (of whom, as of 2009, only 1E9 are using the Internet, incidentally. )
The per capita consumption of energy is 2300 W. We can calculate the total consumption per second for the entire planet:
Total(Earth) = 2.3 E3 * 6.7 E9 ~ 15.E12 W , meaning "about 15 TW" = 15 Terawatts.
The consumption of energy per second by all humans on the planet indeed is about 15 terawatts.
Note: Tera is the international prefix for E12 = the numeral one followed by 12 zeros. You may already be familiar with the prefixes "Mega" and "Giga" in relation to your computer: Megabytes and Gigabytes. From about twenty international prefixes you may want to remember just these four abreviations:M G T P
Mega Giga Tera Peta
E6 E9 E12 E15
How much energy do we all use in a year??? 
The Google search engine understands units of measurement. We can measure time in years, months, hours, or seconds, and Google can calculate the conversions. For example,
We can use that to calculate the total, consumption of energy per year:
If you use this E notation, E with fractional exponents, often, you will develop a feel for the E <-> log mapping:
log 3 ~ .5 log 5 = .7 log 8 = ~ .9
From "person per second" to "planet per year"
We have calculated global use per year (total) by multiplying the rate of the personal consumption (R) by number of people P and then by the number of seconds per year (T): Total = R * P * T .This can also be written as Total = R * (P*T) = R *U , where U= P * T, a universal constant.
We calculate U, a constants, which converts personal rate of anything to global yearly consumption.
To multiply P and T ( U = P*T ) that we the ADD the expnents (as before):
This constant can be use to directly convert per capita rates to global use per year: Per capita 2kW rate of use leads to 2E3 * 213 E15 = 426 E18 Joules per year or 426 PJ, that is 426 petajoules per year .
Other time intervals
Number of seconds in a year, that is 32... millions is a large number, and it is easier to handle when expressed in the E notation, as E7.5. For shorter time intervals, E notation can also make some calculations easier:
| unit | seconds | as E.... | about | |
|---|---|---|---|---|
| hour | 60*60 | E3.5563 | E3.5 | |
| day | 3600*24 | E4.9365 | E5.0 | |
| month | 2592000 | E6.4136 | E6.5 | |
| year | 365*3600*24 | E7.499 | E7.5 |
Here are a few examples how we can use these time interval values expressed in E notations:
If one kwh costs about 10 cents, that means that 1 MJ costs 10/3.6 =27.7 cents ~ $27E-2
E2 W * E5 s = E7 J = 10E6J= 10 MJ. This is ten Megajoules of energy. That is the daily nutritional requirement for a typical man at rest, without exercise or hard physical work.
For comparison, E6J, one Megajoule, is approximately the nutritional value of a snack such as a 65 gram Mars candy bar. A 100 gram dark chocolate Lindt 99% Cacao bar is 2.2E6J, a useful fact if you are considering eating nearly pure chocolate for health reasons.
1 kW= 2 E3 W. A month has E6.4 seconds, so in one month the household uses 1.E3 * E6.4 Ws = E9.4 J = E3.4 MJ
We have calculated above cost of one MJ as $27E-2 $/MJ.
So, cost per month, that the monthly bill is as "nuber of units" * "cost of a unit", i.e.
cost = E3.4 MJ * 27 E-2 $/MJ = 27 E1.4 $= (using calculator) $27 * 25 ~ $675 .
Scientific notation and calculators 
Writing 100 000 as 1. E5 is called "scientific notation." It is used in "scientific calculators." Such calculators are available, as small applications, on computers, on the web, or as a separate gadget looking like the like image on the left. c4s Enter 1E3 or 1000 and press the LOG key and you get 3. Press INV LOG keys and you recover the 1E3. The function 10^x is the INVerse of LOG(x). (See last section for origin of name Log or LOG.)
There is a calculator like this built into some cell phones. One is also built into the Google search engine. Google does not (yet) understand the symbol E. One has to enter 10^3 to obtain
10^3 = 1 000 and log 1000 to get the inverse: log(1000) = 3.
To call a calculator application (a small software program) on your computer, do this:
Units: Metric units and SI units
To measure energy flows, we used as units: Watt with the symbol W.As a units of energy we used: Joule or Ws (wattsecond).
Both are metric units, and both are SI units.
There are several systems of metric units. The "calorie" is also a metric unit of energy, but it is not an SI unit.
From the Babel of different systems, the SI system was selected by the scientific community to be used worldwide. In Europe, the "food calorie" is being phased out in favor of the SI unit of energy, the joule. The US is, as usual, lagging behind the rest of the world in this.
Here are good reasons to use SI units, particularly when working with with large numbers. Because energy comes from many different sources (oil, coal, wood, natural gas, solar, wind, etc.), there are many different units, each tied to a particular fuel. By focusing on the energy content, we can more easily compare different options and the costs of obtaining and using the energy.
These references show how easy it is to compare energy sources once the units of measure are standardized:
Theory, history, and terminology
Note: This section is for those who want to know more or who, perhaps, demand more than the simplified language used in the explanations above.The mathematical foundation justifying the rule "just add the exponents", instead of multiplying the numbers, is based in the principles of decadic logarithms, sometimes called common logarithms or, after the English mathematician, Briggsian logarithms.
Scientific notation, in a more exact use of the term, expresses numbers in the form: a * 10^b , where a is called a significand and b an exponent. Scientific notation uses only integer exponents and it does not have to use E notation, which would write this expression as aEb.
Note that "Engineering notation" is a special case of scientific notation, and uses as an exponents only integers divisible by three.
Avoiding errors introduced by computers The E notation is useful, not only for computer calculations, but anytime when text with numbers is edited or copied on a computer. It helps to eliminate errors which are introduced when expressions such as 10³ or 10^3 are handled by software which ignores the ^ and superscripts. When this happens, expressions such as 10 ^ 3 are misunderstood and come out as 103.
For example, if you "cut and paste" the wikipedia text about carbon dioxide, you get this:
"Carbon dioxide in earth's atmosphere is considered a trace gas currently occurring at an average concentration of about 385 parts per million by volume or 582 parts per million by mass. The mass of the Earth atmosphere is 5.14×1018 kg , so the total mass of atmospheric carbon dioxide is 3.0×1015 kg (3,000 gigatonnes)."
The original text was: "Carbon dioxide in earth's atmosphere is considered a trace gas currently occurring at an average concentration of about 385 parts per million by volume or 582 parts per million by mass. The mass of the Earth atmosphere is 5.14×10^18 kg , so the total mass of atmospheric carbon dioxide is 3.0×10^15 kg (3,000 gigatonnes)."
The numbers 1015 and 108 are errors, caused by careless copying and using the symbol ^, instead of E notation. Such errors are frequent on the Internet. They certainly complicate our discussions of energy! Fractional exponents In this knol we have introduced a logical extension of E notation and used fractional exponents such as E1.5 to represent 10^1.5 = 31.6...
This allows an intuitive grasp of large numbers: It is easy to see that, e.g. E1.510 is slightly larger than E1.405.
Similarly, that e.g. E2.14 is slightly larger than E1.99.
These extensions of E notations combine the use of decadic logarithms and classical E notation in an intuitive way.
Summary In summary, the exponential notation a * 10 ^ b isAll are a form of exponential notation, or E-notation.
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