Numerical Measurements

Numbers

When discussing numbers, it is helpful to know:

The International System of Units (SI)

The International System of Units is the modern form of the metric system [1 page 95] and is abbreviated as SI due its French name of Système International d’Unités [1 page 101]. The SI defines seven base units [1 page 116], several different derived units which are based on the base units [1 pages 117-9], and different prefixes which are used to indicate quantity [1 page 121].

Administering the SI

The table below shows the key organizations for administering the SI ranked from lowest to highest authority [1 page 95] [1 page 101]:

English name French name abbreviation
International Bureau of Weights and Measures Bureau International des Poids et Mesures BIPM
International Committee for Weights and Measures Comité International des Poids et Mesures CIPM
General Conference on Weights and Measures Conférence Générale des Poids et Mesures CGPM

The main purpose of the BIPM "is to define and promote the SI" [1 page 101]. The CIPM supervises the BIPM and reports on the progress of the BIPM to the CGPM [1 page 95].

The SI Prefixes

The SI prefixes are shown below [1 page 121]:

name symbol meaning
yocto y septillionth
zepto z sextillionth
atto a quintillionth
femto f quadrillionth
pico p trillionth
nano n billionth
micro µ millionth
milli m thousandth
centi c hundredth
deci d tenth

deka, which is spelled as deca outside the U.S. [2 page iii] [3]

da ten
hecto h hundred
kilo k thousand
mega M million
giga G billion
tera T trillion
peta P quadrillion
exa E quintillion
zetta Z sextillion
yotta Y septillion

SI prefixes are usable with SI units along with certain non-SI units [1 pages 122+124+127].

Frequency

The SI unit for frequency is hertz (Hz), which means times per second. Hz is a derived unit [1 pages 118] because it's based off of the second (s), an SI base unit [1 page 116].

Length

The SI unit for length is the meter (m) [1 page 116], which is spelled as metre outside the U.S. [2 page iii] [3]. When some form the meter isn't used (mm, cm, m, km, etc.), the inch, foot, yard, or mile is often used instead. The following are the most common length conversion formulas [4]:

The Decibel (dB)

When it comes to measuring intensity and/or power, a unit that is often used is the decibel. The basic gist of measuring something with decibels is that a very low reference value is picked and every 10 decibels indicates a 10 times increase in what's being measured [5] [6]. If you've been keeping up with this article, you might be wondering if a decibel is a tenth of a bel, and the answer is yes. That being said, the decibel is typically used instead of the bel [5] [1 page 127]. The decibel and bel "have been accepted by the CIPM for use with the International System, but are not considered as SI units" [1 page 127].

Data, Data Compression, & Data Overhead

Data, broadly speaking, is any information that is transmitted and/or recorded.

Data compression reduces data size. Lossless compression removes only redundant information, lossy compression removes both redundant and non-redundant information, and perceptually lossless compression removes information in such a way that the loss of information isn't perceived.

Data overhead is additional data that is used to ensure data integrity and/or proper operation of devices.

Bits, Bytes, & Files

Like a number in binary form, digital data is actually a series of 0s and 1s. Each of the 0s and 1s is called a bit, and 8 bits equals one byte. Bits are symbolized with either a lower-case b or the word bit [7]. Bytes are symbolized with an upper-case B [8]. Bits are typically used to measure connection speed, while bytes are typically used to measure storage capacity and file size (a file is a collection of 0 or more bytes).

Prefixes for Bits & Bytes

The SI prefixes of kilo and higher can be applied to bits and bytes. When applied to bits, they typically don't differ in meaning. When applied to bytes, however, the SI prefixes may have a different meaning. Below are the possible meanings of the SI prefixes when applied to bits and bytes [7] [8]:

prefix approximate meaning decimal meaning binary meaning floppy disk meaning
k about a thousand thousand    
K about a thousand thousand 1,024  
M about a million million 1,048,576 1,024,000
G about a billion billion 1,073,741,824  
T about a trillion trillion 1,099,511,627,776  
P about a quadrillion quadrillion 1,125,899,906,842,624  
E about a quintillion quintillion 1,152,921,504,606,846,976  
Z about a sextillion sextillion 1,180,591,620,717,411,303,424  
Y about a septillion septillion 1,208,925,819,614,629,174,706,176  

In order to clear up the confusion resulting from having the same prefix mean different things, special binary prefixes were created. These are shown below [7] [8]:

name symbol meaning
kibi Ki 1,024
mebi Mi 1,048,576
gibi Gi 1,073,741,824
tebi Ti 1,099,511,627,776
pebi Pi 1,125,899,906,842,624
exbi Ei 1,152,921,504,606,846,976
zebi Zi 1,180,591,620,717,411,303,424
yobi Yi 1,208,925,819,614,629,174,706,176

Unless otherwise noted, this website indicates approximate and decimal grouping for bits and bytes with the SI prefixes and binary grouping for bits and bytes with the binary prefixes.

Measuring by the Thousands

Just as the prefix kilo can be used indicate about a thousand, a thousand, or a binary thousand, the letter K (upper-case or lower-case) can be used as a suffix to indicate about a thousand, a thousand, or a binary thousand. 2K, for example, is typically used to refer to 2,000, 2,048, or 2,160, while 4K is typically used to refer to 3,840 or 4,096.

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Sources

1. The International System of Units (SI). 8th edition, 2006. International Bureau of Weights and Measures (BIPM).

2. The International System of Units (SI). Edited by Barry N. Taylor and Ambler Thompson from the original. Mar. 2008. National Institute of Standards and Technology (NIST).

3. American and British English spelling differences. Wikipedia.

4. Imperial and US customary measurement systems. Wikipedia.

5. Decibel. Wikipedia.

6. Joe Wolfe. dB: What is a decibel?. (C) The University of New South Wales (UNSW) School of Physics.

7. Bit. Wikipedia.

8. Byte. Wikipedia.