Number to Scientific Prefix

Convert a numeric value to SI-prefixed text (aka engineering / metric prefix). Bonus: binary prefixes!

The function NUM2SIP converts a numeric scalar into a string with an SI prefix (aka metric prefix, or engineering prefix). For example the value 1000 is converted to '1 k'. The bonus function NUM2BIP converts from numeric to binary-prefixed string, for example the value 1024 is converted to '1 Ki'.

After testing many submissions on MATLAB FEX (see Acknowledgements) and not finding a single one that converted all values correctly and that supported the correct SI spacing, I wrote my own functions. And then exhaustively tested them to confirm that they actually give the correct output.

These functions are particularly useful to help create publications following SI standards, or where control over significant digits and trailing zeros is required, or for including numeric values in figures.

This submission:

• Always includes the space character (required by the SI standard).
• Automatically selects the most suitable prefix.
• Rounds to the requested significant figures (default==5).
• Prefix may be selected as either the full name ('kilo') or the symbol ('k').
• Trailing decimal zeros of the coefficient may be included or removed.
• Rounds up to the next prefix when significant figures require, e.g. '1 M', not '1000 k'.
• Also returns the numeric coefficient and the prefix separately.
• Includes the prefixes added in November 2022: ronna, quetta, ronto, and quecto.

Reverse Conversion

To convert from prefixed string to numeric:

http://www.mathworks.com/matlabcentral/fileexchange/53886-scientific-prefix-to-number

SI Prefix Examples

>> num2sip(10000) % OR num2sip(1e4)
ans = '10 k'
>> num2sip(10000,4,true)
ans = '10 kilo'
>> num2sip(10000,4,false,true)
ans = '10.00 k'

>> num2sip(999,3)
ans = '999 '
>> num2sip(999,2)
ans = '1 k'

>> num2sip(0.5e6)
ans = '500 k'
>> num2sip(0.5e6,[],'M')
ans = '0.5 M'

>> sprintf('Power: %swatt', num2sip(200e6,[],true))
ans = 'Power: 200 megawatt'

>> sprintf('Clock frequency is %sHz.', num2sip(1234567890,3))
ans = 'Clock frequency is 1.23 GHz.'

>> num2sip(sip2num('9 T')) % 9 tera == 9e12 == 9*1000^4
ans = '9 T'

Binary Prefix Examples

>> num2bip(10240) % OR num2bip(1.024e4) OR num2bip(pow2(10,10)) OR num2bip(10*2^10)
ans = '10 Ki'
>> num2bip(10240,4,true)
ans = '10 kibi'
>> num2bip(10240,4,false,true)
ans = '10.00 Ki'

>> num2bip(1023,3)
ans = '1020 '
>> num2bip(1023,2)
ans = '1 Ki'

>> num2bip(pow2(19))
ans = '512 Ki'
>> num2bip(pow2(19),[],'Mi')
ans = '0.5 Mi'

>> sprintf('Memory: %sbyte', num2bip(pow2(200,20),[],true))
ans = 'Memory: 200 mebibyte'

>> sprintf('Data saved in %sB.', num2bip(1234567890,3))
ans = 'Data saved in 1.15 GiB.'

>> num2bip(bip2num('9 Ti')) % 9 tebi == pow2(9,40) == 9*1024^4
ans = '9 Ti'

SI Prefixes (Bureau International des Poids et Mesures)

Magnitude | Symbol | Name

1000^-10 | q | quecto

1000^-9 | r | ronto

1000^-8 | y | yocto

1000^-7 | z | zepto

1000^-6 | a | atto

1000^-5 | f | femto

1000^-4 | p | pico

1000^-3 | n | nano

1000^-2 | µ | micro

1000^-1 | m | milli

1000^0 | |

1000^+1 | k | kilo

1000^+2 | M | mega

1000^+3 | G | giga

1000^+4 | T | tera

1000^+5 | P | peta

1000^+6 | E | exa

1000^+7 | Z | zetta

1000^+8 | Y | yotta

1000^+9 | R | ronna

1000^+10 | Q | quetta

Binary Prefixes (IEC 60027-2 A.2 and ISO/IEC 80000-13:2008)

Magnitude | Symbol | Name

1024^1 | Ki | kibi

1024^2 | Mi | mebi

1024^3 | Gi | gibi

1024^4 | Ti | tebi

1024^5 | Pi | pebi

1024^6 | Ei | exbi

1024^7 | Zi | zebi

1024^8 | Yi | yobi

Notes

These functions have been extensively tested against many edge cases, with particular attention to ensuring the correct rounding for all choices of significant figures. Compared to similar submissions available on MATLAB File Exchange, these functions correctly:

• include the space character following the coefficient, even if there is no prefix (try value 1).
• round to the requested significant figures (try 0.999 or 999e3, with 1 or 2 sigfig).
• return a coefficient without a prefix for zero and values outside the prefix range (try values 0, 7, Inf, 1E99).
• return a coefficient without exponent notation when the significant digits are less than three (try 1e5 to 1 sigfig).