Scientific Notation

Scientific notation is an international convention for making large numbers easy to read. It is frequently used in engineering and programming. It is a subject that every individual should know.

Scientific notation is a shortcut for writing long numbers in a more readable form.

The scientific notation of numbers has the following form;

$$ \mathbb{value} \times 10^{\mathcal{power}} $$

Traditionally, numbers in scientific notation are written with one digit before the decimal point and then the remaining digits. That is, we divide by 10 until the number is less than 10, writing the quotients as exponents.

Since the notation over 10 is difficult in calculators and programming, the letter “e-E” is used for this notation. The following three notations have the same meaning.

$$ 8421000000 = 8.421 \times 10^{9} = 8.421e9 $$

In Turkish, a comma is used as a decimal bracket. In English, a period is used.

Converting a number to scientific notation

Start the base from scratch.
Shift the decimal place until there are no zeros to the left of the decimal and only one place.
- Every time you move to the left, the exponent increases by one.
- Decrease the base by one every time it moves to the right.
Throw out all the leading zeros.
Drop trailing zeros only if the original number has no decimal point.

Scientific Notation in Engineering

In scientific notation in engineering, the exponent of 10 is always written divisible by 3. In this way the prefixes of the SI System of Units can be used. In most calculators the engineering notation is in ENG mode.

IEC and SI Data Size Representations

We know that every electronic device, such as computers and calculators, works in binary. This leads to confusion while reducing data sizes. For this, IEC has published a new abbreviation system, but since the development of computers has been using the decimal base for many years, knowing both helps to avoid confusion. The main factor in the development of this situation is the hardware companies. Hardware companies used a decimal counting system for sales, so that non-technical people could understand it. However, since the binary counting system is valid for computers, this is why the hardware is actually smaller in size when you start using it.

IEC	IEC Symbol	IEC Value	SI	SI Symbol	SI Value
kibibyte	`KiB`	$ 2^{10} $	kilobyte	`kB`	$ 10^{3} $
mebibyte	`MiB`	$ 2^{20} $	megabyte	`MB`	$ 10^{6} $
gibibyte	`GiB`	$ 2^{30} $	gigabyte	`GB`	$ 10^{9} $
tebibyte	`TiB`	$ 2^{40} $	terabyte	`TB`	$ 10^{12} $
pebibyte	`PiB`	$ 2^{50} $	petabyte	`PB`	$ 10^{15} $
exbibyte	`EiB`	$ 2^{60} $	exabyte	`EB`	$ 10^{18} $
zebibyte	`ZiB`	$ 2^{70} $	zettabyte	`ZB`	$ 10^{21} $
yobibyte	`YiB`	$ 2^{80} $	yottabyte	`YB`	$ 10^{24} $

It should be remembered that in programming, if a binary counting system is used for units, IEC should be used, and if a decimal counting system is used, SI should be used.

In the case of file sizes, even if the SI unit system is used for size calculations, 1024 and its multiples should be considered.

Data Sizes

Today we know that hardware uses byte as the smallest unit. This is because when computers were designed, the English alphabet was used. Since ASCI encoding, which includes all English letters, numbers and symbols, was the starting point and 128 different contents had to be represented in binary counting system, 8 bits became the basic data size unit.

In the dimensions below, the SI unit system is used in the nomenclature but according to the binary counting system. So the coefficient is not 1000 but 1024. The original English names are used in the names. In other words, the only difference with IEC is the nomenclature.

Name	Symbol	Bit	B	KB	MB	GB	TB	PB	EB	ZB	YB	RB
Bit	b	`1e0`	`1.25e-1`	`1.220703125e-4`	`1.1920928955078125e-7`	`1.16415321826934814453125e-10`	`1.136868377216160297393798828125e-13`	`1.1102230246251565404236316680908203125e-16`	`1.08420217248550443400745280086994171142578125e-19`	`1.058791184067875423835403125849552452564239501953125e-22`	`1.0339757656912845935892608650874535669572651386260986328125e-25`	`1.00974195868289511092701256356196637398170423693954944610595703125e-28`
Nibble	N	`4e0`	`5e-1`	`4.8828125e-4`	`4.76837158203125e-7`	`4.656612873077392578125e-10`	`4.5474735088646411895751953125e-13`	`4.44089209850062616169452667236328125e-16`	`4.336808689942017736029811203479766845703125e-19`	`4.2351647362715016953416125033982098102569580078125e-22`	`4.13590306276513837435704346034981426782906055450439453125e-25`	`4.038967834731580443708050254247865495926816947758197784423828125e-28`
Byte	B	`8e0`	`1e0`	`9.765625e-4`	`9.5367431640625e-7`	`9.31322574615478515625e-10`	`9.094947017729282379150390625e-13`	`8.8817841970012523233890533447265625e-16`	`8.67361737988403547205962240695953369140625e-19`	`8.470329472543003390683225006796419620513916015625e-22`	`8.2718061255302767487140869206996285356581211090087890625e-25`	`8.07793566946316088741610050849573099185363389551639556884765625e-28`
Kilobyte	KB	`8.192e3`	`1,024`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`1`	`0`
Megabyte	MB	`8.388608e6`	`1,048,576`	`1,024`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`
Gigabyte	GB	`8.589934592e9`	`1,073,741,824`	`1,048,576`	`1,024`	`0`	`0`	`0`	`0`	`0`	`0`	`0`
Terabyte	TB	`8.796093022208e12`	`1,099,511,627,776`	`1,024`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`
Petabyte	PB	`9.007199254740992e15`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`
Exabyte	EB	`9.223372036854775808e18`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`
Zettabyte	ZB	`9.444732965739290427392e21`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`
Yottabyte	YB	`9.671406556917033397649408e24`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`
Ronnabyte	RB	`9.903520314283042199192993792e27`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`
Quettabyte	QB	`1.0141204801825835211973625643008e31`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`	`0`

Sources

[https://physics.nist.gov/cuu/Units/binary.html](https://physics.nist.gov/cuu/Units/binary.html)

[https://en.wikipedia.org/wiki/Si_prefix](https://en.wikipedia.org/wiki/Si_prefix)

[https://en.wikipedia.org/wiki/Binary_prefix](https://en.wikipedia.org/wiki/Binary_prefix)

Taken from UCH Viki. ===== NOTLAR ===== Kaynakları belirtmek için özel bir tema hazırlandığında sondaki kaynaklar düzeltilecek.

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