Digit of 0 before a number
A
leading zero
is any
0
digit
that comes before the first nonzero digit in a number string in
positional notation
.
[1]
For example,
James Bond
's famous identifier, 007, has two leading zeros.
[2]
Any zeroes appearing to the left of the first non-zero digit (of any integer or decimal) do not affect its value, and can be omitted (or replaced with blanks) with no loss of information.
[3]
Therefore, the usual
decimal
notation of
integers
does not use leading zeros except for the
zero itself
, which would be denoted as an
empty string
otherwise.
[4]
However, in
decimal fractions
strictly between ?1 and 1, the leading zeros digits between the
decimal point
and the first nonzero digit are necessary for conveying the magnitude of a number and cannot be omitted,
[1]
while
trailing zeros
? zeros occurring after the decimal point and after the last nonzero digit ? can be omitted without changing the meaning.
Occurrence
[
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]
Often, leading zeros are found on non-electronic
digital displays
or on such electronic ones as
seven-segment displays
, that contain fixed sets of digits. These devices include manual counters,
stopwatches
,
[5]
odometers
,
[6]
and
digital clocks
.
[5]
Leading zeros are also generated by many older computer programs when creating values to assign to new records, accounts and other files, and as such are likely to be used by utility billing systems, human resources information systems and government databases. Many
digital cameras
and other electronic media recording devices use leading zeros when creating and saving new files to make names of the equal length.
Leading zeros are also present whenever the number of digits is fixed by the technical system (such as in a
memory register
), but the stored value is not large enough to result in a non-zero
most significant digit
.
[7]
The
count leading zeros
operation efficiently determines the number of leading zero
bits
in a
machine word
.
[8]
A leading zero appears in
roulette
in the United States, where "00" is distinct from "0" (a wager on "0" will not win if the ball lands in "00", and vice versa). Sports where competitors are numbered follow this as well; a
stock car
numbered "07" would be considered distinct from one numbered "7".
Benito Santiago
, a
Major League Baseball
catcher who wore the number 09 for several years, is the only
major professional sports league
player to use a
jersey number
with a leading zero, not counting several who have worn the number 00 (he wore the extra zero to avoid complications with his catcher's pads, allowing the back strap to run between the numbers instead of over a single digit 9).
Dennis Rodman
had requested the number 01 when he joined the
Chicago Bulls
(as his usual number 10 had already been retired), but the
National Basketball Association
forbade it, and Rodman instead wore 91.
[9]
In most countries other than the United States, numbers between 0 and 1, expressed as a decimal, include a zero before the decimal point (e.g. 0.64 or in many countries 0,64) while in the United States this zero is often omitted (.64).
Advantages
[
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]
Collation
[
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]
Leading zeros are used to make ascending order of numbers correspond with
alphabetical order
: e.g., 11 comes alphabetically before 2, but after 02. (See, e.g.,
ISO 8601
.) This does not work with
negative numbers
, though, whether leading zeros are used or not: −23 comes alphabetically after −01, −1, and −22, although it is less than all of them.
Error prevention
[
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]
Leading zeros in a sentence also make it less likely that a careless reader will overlook the decimal point. For example, in modern
pharmacy
there is a widely followed convention that leading zeros before a decimal must not be omitted from any
dose
or dosage value in
drug prescribing
(e.g.
0.2
mg
must be used, not
.2 mg
). Meanwhile,
trailing zeros
are forbidden (e.g.
2 mg
must be used, not
2.0 mg
). In both cases, the intention is to prevent misreading and the resultant misdose by one or several
orders of magnitude
.
[10]
Fraud prevention
[
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]
Leading zeros can also be used to prevent fraud by filling in character positions that might normally be empty. For example, adding leading zeros to the amount of a
check
(or similar financial document) makes it more difficult for fraudsters to alter the amount of the check before presenting it for payment.
Zero as a prefix
[
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]
A prefix
0
is used in
C
to specify string representations of
octal
numbers, as required by the
ANSI C
standard for the
strtol()
function (which converts strings to long integers) in the
<stdlib.h>
library.
[11]
Many other programming languages, such as
Python
,
Perl
,
Ruby
,
PHP
, and the Unix shell
bash
also follow this specification for converting strings to numbers. As an example, "
0020
" does not represent 20
10
(
2
×10
1
+
0
×10
0
), but rather 20
8
= 16
10
(
2
×8
1
+
0
×8
0
=
1
×10
1
+
6
×10
0
). Decimal numbers written with leading zeros will be interpreted as octal by languages that follow this convention and will generate errors if they contain "8" or "9", since these digits do not exist in octal. This behavior can be a nuisance when working with sequences of strings with embedded, zero-padded
decimal
numbers (typically file names) to facilitate alphabetical sorting (see above) or when validating inputs from users who would not know that adding a leading zero triggers this base conversion.
See also
[
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]
References
[
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]
- ^
a
b
Miller, Jane E. (2008),
The Chicago Guide to Writing about Numbers
, University of Chicago Press, p. 276,
ISBN
9780226526324
.
- ^
Lafore, Robert W.
(1987),
Microsoft C: programming for the IBM
, H.W. Sams, p.
294
,
ISBN
9780672225154
.
- ^
Zegarelli, Mark (2014),
Basic Math and Pre-Algebra Workbook For Dummies
(2nd ed.), John Wiley & Sons, p. 8,
ISBN
9781118828304
.
- ^
Flynt, Clif (2012),
Tcl/Tk: A Developer's Guide
, Elsevier, pp. 752?753,
ISBN
9780123847171
.
- ^
a
b
Greene, Jennifer; Stellman, Andrew (2013),
Head First C#
, O'Reilly Media, Inc., p. 770,
ISBN
9781449358884
.
- ^
Dueck, Robert; Reid, Ken (2011),
Digital Electronics
, Cengage Learning, p. 48,
ISBN
9781133708964
.
- ^
Kuc, Roman (1999),
The digital information age: an introduction to electrical engineering
, PWS Pub. Co., p.
67
,
ISBN
9780534953157
.
- ^
Dandamudi, Sivarama P. (2005),
Guide to RISC Processors: for Programmers and Engineers
, Springer, p. 139,
ISBN
9780387274461
.
- ^
Armour, Terry.
Joining Bulls `Almost Like A Storybook' For Former Collins Prep Brown
Archived
June 4, 2015, at the
Wayback Machine
. October 6, 1995
- ^
Davis, Neil M. (2005).
Medical Abbreviations: 26,000 Conveniences at the Expense of Communication and Safety
(12th ed.). Warminster, PA: Neil M. Davis Associates. p. 7.
ISBN
0931431123
.
- ^
Kernighan, Brian
;
Ritchie, Dennis M.
(March 1988).
The C Programming Language
(2nd ed.).
Englewood Cliffs, NJ
:
Prentice Hall
. p. 252.
ISBN
0-13-110362-8
.